Academic Commons Search Results
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Academic Commons Search Resultsen-usComment: Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies
http://academiccommons.columbia.edu/catalog/ac:184983
Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D84T6H8MSat, 28 Mar 2015 00:00:00 +0000The authors suggest an interesting way to measure the fraction of missing information in the context of hypothesis testing. The measure seeks to quantify the impact of missing observations on the test between two hypotheses. The amount of impact can be useful information for applied research. An example is, in genetics, where multiple tests of the same sort are performed on different variables with different missing rates, and follow-up studies may be designed to resolve missing values in selected variables. In this discussion, we offer our prospective views on the use of relative information in a follow-up study. For studies where the impact of missing observations varies greatly across different variables and where the investigators have the flexibility of designing studies that can have different efforts on variables, an optimal design may be derived using relative information measures to improve the cost-effectiveness of the followup.Statisticstz33, shl5StatisticsArticlesBayesian hierarchical graph-structured model for pathway analysis using gene expression data
http://academiccommons.columbia.edu/catalog/ac:184980
Zhou, Hui; Zheng, Tianhttp://dx.doi.org/10.7916/D8DB80QNSat, 28 Mar 2015 00:00:00 +0000In genomic analysis, there is growing interest in network structures that represent biochemistry interactions. Graph structured or constrained inference takes advantage of a known relational structure among variables to introduce smoothness and reduce complexity in modeling, especially for high-dimensional genomic data. There has been a lot of interest in its application in model regularization and selection. However, prior knowledge on the graphical structure among the variables can be limited and partial. Empirical data may suggest variations and modifications to such a graph, which could lead to new and interesting biological findings. In this paper, we propose a Bayesian random graph-constrained model, rGrace, an extension from the Grace model, to combine a priori network information with empirical evidence, for applications such as pathway analysis. Using both simulations and real data examples, we show that the new method, while leading to improved predictive performance, can identify discrepancy between data and a prior known graph structure and suggest modifications and updates.Biostatistics, Geneticstz33StatisticsArticlesDiscovering interactions among BRCA1 and other candidate genes associated with sporadic breast cancer
http://academiccommons.columbia.edu/catalog/ac:184992
Lo, Shaw-Hwa; Chernoff, Herman; Cong, Lei; Ding, Yuejing; Zheng, Tianhttp://dx.doi.org/10.7916/D8CC0ZKFSat, 28 Mar 2015 00:00:00 +0000Analysis of a subset of case-control sporadic breast cancer data, [from the National Cancer Institute's Cancer Genetic Markers of Susceptibility (CGEMS) initiative], focusing on 18 breast cancer-related genes with 304 SNPs, indicates that there are many interesting interactions that form two- and three-way networks in which BRCA1 plays a dominant and central role. The apparent interactions of BRCA1 with many other genes suggests the conjecture that BRCA1 serves as a protective gene and that some mutations in it or in related genes may prevent it from carrying out this protective function even if the patients are not carriers of known cancer-predisposing BRCA1 mutations. The method of analysis features the evaluation of the effect of a gene by averaging the effects of the SNPs covered by that gene. Marginal methods that test one gene at a time fail to show any effect. That may be related to the fact that each of these 18 genes adds very little to the risk of cancer. Analysis that relates the ratio of interactions to the maximum of the first-order effects discovers significant gene pairs and triplets. Breast cancer (MIM 114480) has complex causes. Known predisposition genes explain <15% of the breast cancer cases. It is generally believed that most sporadic breast cancers are triggered by unknown combined effects, possibly because of a large number of genes and other risk factors, each adding a small risk toward cancer etiology. Progress in seeking breast cancer genes other than BRCA1 and BRCA2 has been slow and limited because the individual risk due to each gene is small. This difficulty may be partly due to the fact that current methods rely largely on marginal information from genes studied one at a time and ignore potentially valuable information because of the interaction among multiple loci. Because each responsible gene may have a small marginal effect in causing disease, it is likely that such methods will fail to capture many responsible genes by studying a dataset where the disease may be due to a variety of different sources. The possible presence of many genes responsible for different subgroups of cancer patients may reduce the power of current methods to detect genes partly responsible for some forms of breast cancer. It is believed that methods effective in extracting interactive information from data should be developed. What should be done when marginal effects are too weak to be detected? Our methods use interactive information from multiple sites as well as marginal information, They provide power to detect interactive genes. To test this claim and to demonstrate the practical value of these methods in real applications, we apply them to an important study: a subset of a large dataset collected from a case-control sporadic breast cancer study, focusing on gene–gene-based analysis. This partial dataset comprises 18 genes with 304 SNP markers. The application results in a number of scientific findings. The message of this article is fourfold. First, if marginal methods fail, more powerful methods that take into account interactive information can be used effectively. We apply our proposed methods to this dataset to illustrate the detection of the interactions between genes. We point out that in our findings, none of the 18 selected genes show any detectable marginal effects that are significantly higher than those generated by random fluctuations. In other words, all of the 18 genes would be missed if only marginal methods were used. Second, we demonstrate how to carry out a gene-based analysis by treating each gene as a basic unit while incorporating relevant information from all SNPs within that gene. Two summary test scores are proposed to quantify the strength of interactions for each pair of genes. The pairwise interactions can be extended easily. We also provide results using third-order interactions. Third, to establish statistical significance, we generate a large number of permutations of the dependent variable (case or control) to see how the measures of interaction for the real data compare with those from the many permutations. Finally, when these procedures are applied to the data, they lead to a number of interesting findings. It is shown that there are a substantial number of significant interactions that form a network in which BRCA1 plays a dominant role. The interactions of BRCA1 with many of the other genes suggests the conjecture that BRCA1 serves as a protective gene and that some mutations in it or in related genes may prevent it from carrying out the protective function.Biostatistics, Geneticsshl5, tz33StatisticsArticlesProbing genetic overlap among complex human phenotypes
http://academiccommons.columbia.edu/catalog/ac:184989
Rzhetsky, Andrey; Wajngurt, David; Park, Naeun; Zheng, Tianhttp://dx.doi.org/10.7916/D8MS3RPRSat, 28 Mar 2015 00:00:00 +0000Geneticists and epidemiologists often observe that certain hereditary disorders cooccur in individual patients significantly more (or significantly less) frequently than expected, suggesting there is a genetic variation that predisposes its bearer to multiple disorders, or that protects against some disorders while predisposing to others. We suggest that, by using a large number of phenotypic observations about multiple disorders and an appropriate statistical model, we can infer genetic overlaps between phenotypes. Our proof-of-concept analysis of 1.5 million patient records and 161 disorders indicates that disease phenotypes form a highly connected network of strong pairwise correlations. Our modeling approach, under appropriate assumptions, allows us to estimate from these correlations the size of putative genetic overlaps. For example, we suggest that autism, bipolar disorder, and schizophrenia share significant genetic overlaps. Our disease network hypothesis can be immediately exploited in the design of genetic mapping approaches that involve joint linkage or association analyses of multiple seemingly disparate phenotypes.Biostatistics, Geneticstz33StatisticsArticlesA demonstration and findings of a statistical approach through reanalysis of inflammatory bowel disease data
http://academiccommons.columbia.edu/catalog/ac:184986
Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8W95829Sat, 28 Mar 2015 00:00:00 +0000We test the backward haplotype transmission association algorithm on genome-scan data previously studied by Rioux et al. [Rioux, J. D., et al. (2000) Am. J. Hum. Genet. 66, 1863–1870]. In their study, multipoint linkage methods were applied to affected sib-pairs with inflammatory bowel disease, and significant linkage evidence points to two susceptibility loci. After we apply our approach to these data with a global search accounting for both joint and marginal effects, very interesting results emerge, many of them intriguing. These results provide compelling support for the application of our approach to other data wherever applicable. Results from this project also make it clear that it is important to reinvestigate available family-based datasets that can be suitably reanalyzed. Given previously collected data in the literature, our approach, with its increased efficiency in using available resources, draws additional crucial information that may lead to novel and surprising results.Biostatistics, Geneticsshl5, tz33StatisticsArticlesSelecting informative genes for discriminant analysis using multigene expression profiles.
http://academiccommons.columbia.edu/catalog/ac:184902
Yan, Xin; Zheng, Tianhttp://dx.doi.org/10.7916/D8XK8DF3Fri, 27 Mar 2015 00:00:00 +0000Gene expression data extracted from microarray experiments have been used to study the difference between mRNA abundance of genes under different conditions. In one of such experiments, thousands of genes are measured simultaneously, which provides a high-dimensional feature space for discriminating between different sample classes. However, most of these dimensions are not informative about the between-class difference, and add noises to the discriminant analysis. In this paper we propose and study feature selection methods that evaluate the "informativeness" of a set of genes. Two measures of information based on multigene expression profiles are considered for a backward information-driven screening approach for selecting important gene features. By considering multigene expression profiles, we are able to utilize interaction information among these genes. Using a breast cancer data, we illustrate our methods and compare them to the performance of existing methods. We illustrate in this paper that methods considering gene-gene interactions have better classification power in gene expression analysis. In our results, we identify important genes with relative large p-values from single gene tests. This indicates that these are genes with weak marginal information but strong interaction information, which will be overlooked by strategies that only examine individual genes.Biostatistics, Geneticstz33StatisticsArticlesIdentifying rare disease variants in the Genetic Analysis Workshop 17 simulated data: a comparison of several statistical approaches
http://academiccommons.columbia.edu/catalog/ac:184928
Fan, Ruixue; Huang, Chien-Hsun; Lo, Shaw-Hwa; Zheng, Tian; Ionita-Laza, Iulianahttp://dx.doi.org/10.7916/D89P30J1Fri, 27 Mar 2015 00:00:00 +0000Genome-wide association studies have been successful at identifying common disease variants associated with complex diseases, but the common variants identified have small effect sizes and account for only a small fraction of the estimated heritability for common diseases. Theoretical and empirical studies suggest that rare variants, which are much less frequent in populations and are poorly captured by single-nucleotide polymorphism chips, could play a significant role in complex diseases. Several new statistical methods have been developed for the analysis of rare variants, for example, the combined multivariate and collapsing method, the weighted-sum method and a replication-based method. Here, we apply and compare these methods to the simulated data sets of Genetic Analysis Workshop 17 and thereby explore the contribution of rare variants to disease risk. In addition, we investigate the usefulness of extreme phenotypes in identifying rare risk variants when dealing with quantitative traits. Finally, we perform a pathway analysis and show the importance of the vascular endothelial growth factor pathway in explaining different phenotypes.Genetics, Biostatisticsrf2283, shl5, tz33, ii2135Statistics, BiostatisticsArticlesIdentifying influential regions in extremely rare variants using a fixed-bin approach
http://academiccommons.columbia.edu/catalog/ac:184917
Agne, Michael; Huang, Chien-Hsun; Hu, Inchi; Wang, Haitian; Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D8VM4B5WFri, 27 Mar 2015 00:00:00 +0000In this study, we analyze the Genetic Analysis Workshop 17 data to identify regions of single-nucleotide polymorphisms (SNPs) that exhibit a significant influence on response rate (proportion of subjects with an affirmative affected status), called the affected ratio, among rare variants. Under the null hypothesis, the distribution of rare variants is assumed to be uniform over case (affected) and control (unaffected) subjects. We attempt to pinpoint regions where the composition is significantly different between case and control events, specifically where there are unusually high numbers of rare variants among affected subjects. We focus on private variants, which require a degree of “collapsing” to combine information over several SNPs, to obtain meaningful results. Instead of implementing a gene-based approach, where regions would vary in size and sometimes be too small to achieve a strong enough signal, we implement a fixed-bin approach, with a preset number of SNPs per region, relying on the assumption that proximity and similarity go hand in hand. Through application of 100-SNP and 30-SNP fixed bins, we identify several most influential regions, which later are seen to contain some of the causal SNPs. The 100- and 30-SNP approaches detected seven and three causal SNPs among the most significant regions, respectively, with two overlapping SNPs located in the ELAVL4 gene, reported by both procedures.Genetics, Biostatisticsmra2110, tz33, shl5StatisticsArticlesAssociation screening for genes with multiple potentially rare variants: an inverse-probability weighted clustering approach
http://academiccommons.columbia.edu/catalog/ac:184921
Liu, Ying; Huang, Chien-Hsun; Hu, Inchi; Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D8BP01QVFri, 27 Mar 2015 00:00:00 +0000Both common variants and rare variants are involved in the etiology of most complex diseases in humans. Developments in sequencing technology have led to the identification of a high density of rare variant single-nucleotide polymorphisms (SNPs) on the genome, each of which affects only at most 1% of the population. Genotypes derived from these SNPs allow one to study the involvement of rare variants in common human disorders. Here, we propose an association screening approach that treats genes as units of analysis. SNPs within a gene are used to create partitions of individuals, and inverse-probability weighting is used to overweight genotypic differences observed on rare variants. Association between a phenotype trait and the constructed partition is then evaluated. We consider three association tests (one-way ANOVA, chi-square test, and the partition retention method) and compare these strategies using the simulated data from the Genetic Analysis Workshop 17. Several genes that contain causal SNPs were identified by the proposed method as top genes.Genetics, Biostatisticsyl2802, tz33, shl5Statistics, BiostatisticsArticlesJoint study of genetic regulators for expression traits related to breast cancer
http://academiccommons.columbia.edu/catalog/ac:184947
Zheng, Tian; Wang, Shuang; Cong, Lei; Ding, Yuejing; Ionita-Laza, Iuliana; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D86T0KHXFri, 27 Mar 2015 00:00:00 +0000The mRNA expression levels of genes have been shown to have discriminating power for the classification of breast cancer. Studying the heritability of gene expression levels on breast cancer related transcripts can lead to the identification of shared common regulators and inter-regulation patterns, which would be important for dissecting the etiology of breast cancer. We applied multilocus association genome-wide scans to 18 breast cancer related transcripts and combined the results with traditional linkage scans. Regulatory hotspots for these transcripts were identified and some inter-regulation patterns were observed. We also derived evidence on interacting genetic regulatory loci shared by a number of these transcripts. In this paper, by restricting to a set of related genes, we were able to employ a more detailed multilocus approach that evaluates both marginal and interaction association signals at each single-nucleotide polymorphism. Interesting inter-regulation patterns and significant overlaps of genetic regulators between transcripts were observed. Interaction association results returned more expression quantitative trait locus hotspots that are significant.Genetics, Biostatisticstz33, sw2206, ii2135, shl5Statistics, BiostatisticsArticlesTranscription activity hot spot, is it real or an artifact?
http://academiccommons.columbia.edu/catalog/ac:184944
Wang, Shuang; Zheng, Tian; Wang, Yuanjiahttp://dx.doi.org/10.7916/D808647VFri, 27 Mar 2015 00:00:00 +0000Transcription activity 'hot spots', defined as chromosome regions that contain more expression quantitative trait loci than would have been expected by chance, have been frequently detected both in humans and in model organisms. It has been common to consider the existence of hot spots as evidence for master regulation of gene expression. However, hot spots could also simply be due to highly correlated gene expressions or linkage disequilibrium and do not truly represent master regulators. A recent simulation study using real human gene expression data but simulated random single-nucleotide polymorphism genotypes showed patterns of clustering of expression quantitative trait loci that resemble those in actual studies [Perez-Enciso: Genetics 2004, 166: 547–554.]. In this study, to assess the credibility of transcription activity hot spots, we conducted genetic analyses on gene expressions provided by Genetic Analysis Workshop 15 Problem 1.Genetics, Biostatisticssw2206, tz33, yw2016Statistics, BiostatisticsArticlesNew insights into old methods for identifying causal rare variants
http://academiccommons.columbia.edu/catalog/ac:184925
Wang, Haitian; Huang, Chien-Hsun; Lo, Shaw-Hwa; Zheng, Tian; Hu, Inchihttp://dx.doi.org/10.7916/D8K64H03Fri, 27 Mar 2015 00:00:00 +0000The advance of high-throughput next-generation sequencing technology makes possible the analysis of rare variants. However, the investigation of rare variants in unrelated-individuals data sets faces the challenge of low power, and most methods circumvent the difficulty by using various collapsing procedures based on genes, pathways, or gene clusters. We suggest a new way to identify causal rare variants using the F-statistic and sliced inverse regression. The procedure is tested on the data set provided by the Genetic Analysis Workshop 17 (GAW17). After preliminary data reduction, we ranked markers according to their F-statistic values. Top-ranked markers were then subjected to sliced inverse regression, and those with higher absolute coefficients in the most significant sliced inverse regression direction were selected. The procedure yields good false discovery rates for the GAW17 data and thus is a promising method for future study on rare variants.Genetics, Biostatisticsshl5, tz33StatisticsArticlesConstructing gene association networks for rheumatoid arthritis using the backward genotype-trait association (BGTA) algorithm
http://academiccommons.columbia.edu/catalog/ac:184950
Ding, Yuejing; Cong, Lei; Ionita-Laza, Iuliana; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8Z89B92Fri, 27 Mar 2015 00:00:00 +0000Rheumatoid arthritis (RA, MIM 180300) is a common and complex inflammatory disorder. The North American Rheumatoid Arthritis Consortium (NARAC) data, as part of the Genetic Analysis Workshop 15 data, consists of both genome scan and candidate gene studies on RA patients. We applied the backward genotype-trait association (BGTA) algorithm to capture marginal and gene × gene interaction effects of multiple susceptibility loci on RA disease status. A two-stage screening approach was used for the genome scan, whereas a comprehensive study of all possible subsets was conducted for the candidate genes. For the genome scan, we constructed an association network among 39 genetic loci that demonstrated strong signals, 19 of which have been reported in the RA literature. For the candidate genes, we found strong signals for PTPN22 and SUMO4. Based on significant association evidence, we built an association network among the loci of PTPN22, PADI4, DLG5, SLC22A4, SUMO4, and CARD15. To control for false positives, we used permutation tests to constrain the family-wise type I error rate to 1%. Using the BGTA algorithm, we identified genetic loci and candidate genes that were associated with RA susceptibility and association networks among them. For the first time, we report possible interactions between single-nucleotide polymorphisms/genes, which may be useful for biological interpretation.Genetics, Biostatisticsii2135, shl5, tz33Statistics, BiostatisticsArticlesRheumatoid arthritis-associated gene-gene interaction network for rheumatoid arthritis candidate genes
http://academiccommons.columbia.edu/catalog/ac:184935
Huang, Chien-Hsun; Cong, Lei; Xie, Jun; Qiao, Bo; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8J67FTVFri, 27 Mar 2015 00:00:00 +0000Rheumatoid arthritis (RA, MIM 180300) is a chronic and complex autoimmune disease. Using the North American Rheumatoid Arthritis Consortium (NARAC) data set provided in Genetic Analysis Workshop 16 (GAW16), we used the genotype-trait distortion (GTD) scores and proposed analysis procedures to capture the gene-gene interaction effects of multiple susceptibility gene regions on RA. In this paper, we focused on 27 RA candidate gene regions (531 SNPs) based on a literature search. Statistical significance was evaluated using 1000 permutations. HLADRB1 was found to have strong marginal association with RA. We identified 14 significant interactions (p < 0.01), which were aggregated into an association network among 12 selected candidate genes PADI4, FCGR3, TNFRSF1B, ITGAV, BTLA, SLC22A4, IL3, VEGF, TNF, NFKBIL1, TRAF1-C5, and MIF. Based on our and other contributors' findings during the GAW16 conference, we further studied 24 candidate regions with 336 SNPs. We found 23 significant interactions (p-value < 0.01), nine interactions in addition to our initial findings, and the association network was extended to include candidate genes HLA-A, HLA-B, HLA-C, CTLA4, and IL6. As we will discuss in this paper, the reported possible interactions between genes may suggest potential biological activities of RA.Genetics, Biostatisticsshl5, tz33StatisticsArticlesPattern-based mining strategy to detect multi-locus association and gene × environment interaction
http://academiccommons.columbia.edu/catalog/ac:184941
Li, Zhong; Zheng, Tian; Califano, Andrea; Floratos, Aristidishttp://dx.doi.org/10.7916/D8H70DQGFri, 27 Mar 2015 00:00:00 +0000As genome-wide association studies grow in popularity for the identification of genetic factors for common and rare diseases, analytical methods to comb through large numbers of genetic variants efficiently to identify disease association are increasingly in demand. We have developed a pattern-based data-mining approach to discover unlinked multilocus genetic effects for complex disease and to detect genotype × phenotype/genotype × environment interactions. On a densely mapped chromosome 18 data set for rheumatoid arthritis that was made available by Genetic Analysis Workshop 15, this method detected two potential two-locus associations as well as a putative two-locus gene × gender interaction.Genetics, Biostatisticszl2147, tz33, ac2248, af2202Statistics, Biomedical Informatics, Systems BiologyArticlesGenome-wide gene-based analysis of rheumatoid arthritis-associated interaction with PTPN22 and HLA-DRB1
http://academiccommons.columbia.edu/catalog/ac:184932
Qiao, Bo; Huang, Chien-Hsun; Cong, Lei; Xie, Jun; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8SQ8Z92Fri, 27 Mar 2015 00:00:00 +0000The genes PTPN22 and HLA-DRB1 have been found by a number of studies to confer an increased risk for rheumatoid arthritis (RA), which indicates that both genes play an important role in RA etiology. It is believed that they not only have strong association with RA individually, but also interact with other related genes that have not been found to have predisposing RA mutations. In this paper, we conduct genome-wide searches for RA-associated gene-gene interactions that involve PTPN22 or HLA-DRB1 using the Genetic Analysis Workshop 16 Problem 1 data from the North American Rheumatoid Arthritis Consortium. MGC13017, HSPCAL3, MIA, PTPNS1L, and IGLVI-70, which showed association with RA in previous studies, have been confirmed in our analysis.Genetics, Biostatisticsshl5, tz33StatisticsArticlesDiscovering pure gene-environment interactions in blood pressure genome-wide association studies data: a two-step approach incorporating new statistics
http://academiccommons.columbia.edu/catalog/ac:184905
Wang, Maggie Haitan; Huang, Chien-Hsun; Zheng, Tian; Lo, Shaw-Hwa; Hu, Inchihttp://dx.doi.org/10.7916/D8DN43X5Fri, 27 Mar 2015 00:00:00 +0000Environment has long been known to play an important part in disease etiology. However, not many genome-wide association studies take environmental factors into consideration. There is also a need for new methods to identify the gene-environment interactions. In this study, we propose a 2-step approach incorporating an influence measure that capturespure gene-environment effect. We found that pure gene-age interaction has a stronger association than considering the genetic effect alone for systolic blood pressure, measured by counting the number of single-nucleotide polymorphisms (SNPs)reaching a certain significance level. We analyzed the subjects by dividing them into two age groups and found no overlap in the top identified SNPs between them. This suggested that age might have a nonlinear effect on genetic association. Furthermore, the scores of the top SNPs for the two age subgroups were about 3times those obtained when using all subjects for systolic blood pressure. In addition, the scores of the older age subgroup were much higher than those for the younger group. The results suggest that genetic effects are stronger in older age and that genetic association studies should take environmental effects into consideration, especially age.Genetics, Biostatisticstz33, shl5StatisticsArticlesConsidering interactive effects in the identification of influential regions with extremely rare variants via fixed bin approach
http://academiccommons.columbia.edu/catalog/ac:184914
Agne, Michael; Huang, Chien-Hsun; Hu, Inchi; Wang, Haitian; Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D8445KCHFri, 27 Mar 2015 00:00:00 +0000In this study, we analyze the Genetic Analysis Workshop 18 (GAW18) data to identify regions of single-nucleotide polymorphisms (SNPs), which significantly influence hypertension status among individuals. We have studied the marginal impact of these regions on disease status in the past, but we extend the method to deal with environmental factors present in data collected over several exam periods. We consider the respective interactions between such traits as smoking status and age with the genetic information and hope to augment those genetic regions deemed influential marginally with those that contribute via an interactive effect. In particular, we focus only on rare variants and apply a procedure to combine signal among rare variants in a number of "fixed bins" along the chromosome. We extend the procedure in Agne et al to incorporate environmental factors by dichotomizing subjects via traits such as smoking status and age, running the marginal procedure among each respective category (i.e., smokers or nonsmokers), and then combining their scores into a score for interaction. To avoid overlap of subjects, we examine each exam period individually. Out of a possible 629 fixed-bin regions in chromosome 3, we observe that 11 show up in multiple exam periods for gene-smoking score. Fifteen regions exhibit significance for multiple exam periods for gene-age score, with 4 regions deemed significant for all 3 exam periods. The procedure pinpoints SNPs in 8 "answer" genes, with 5 of these showing up as significant in multiple testing schemes (Gene-Smoking, Gene-Age for Exams 1, 2, and 3).Genetics, Biostatisticsmra2110, tz33, shl5StatisticsArticlesA dual-clustering framework for association screening with whole genome sequencing data and longitudinal traits
http://academiccommons.columbia.edu/catalog/ac:184911
Lui, Ying; Huang, Chien-Hsun; Hu, Inchi; Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D8N29VVKFri, 27 Mar 2015 00:00:00 +0000Current sequencing technology enables generation of whole genome sequencing data sets that contain a high density of rare variants, each of which is carried by, at most, 5% of the sampled subjects. Such variants are involved in the etiology of most common diseases in humans. These diseases can be studied by relevant longitudinal phenotype traits. Tests for association between such genotype information and longitudinal traits allow the study of the function of rare variants in complex human disorders. In this paper, we propose an association-screening framework that highlights the genotypic differences observed on rare variants and the longitudinal nature of phenotypes. In particular, both variants within a gene and longitudinal phenotypes are used to create partitions of subjects. Association between the 2 sets of constructed partitions is then evaluated. We apply the proposed strategy to the simulated data from the Genetic Analysis Workshop 18 and compare the obtained results with those from sequence kernel association test using the receiver operating characteristic curves.Genetics, Biostatisticstz33, shl5StatisticsArticlesA partition-based approach to identify gene-environment interactions in genome wide association studies
http://academiccommons.columbia.edu/catalog/ac:184908
Fan, Ruixue; Huang, Chien-Hsun; Hu, Inchi; Wang, Haitan; Zheng, Tian; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D8542MGFFri, 27 Mar 2015 00:00:00 +0000It is believed that almost all common diseases are the consequence of complex interactions between genetic markers and environmental factors. However, few such interactions have been documented to date. Conventional statistical methods for detecting gene and environmental interactions are often based on the linear regression model, which assumes a linear interaction effect. In this study, we propose a nonparametric partition-based approach that is able to capture complex interaction patterns. We apply this method to the real data set of hypertension provided by Genetic Analysis Workshop 18. Compared with the linear regression model, the proposed approach is able to identify many additional variants with significant gene-environmental interaction effects. We further investigate one single-nucleotide polymorphism identified by our method and show that its gene-environmental interaction effect is, indeed, nonlinear. To adjust for the family dependence of phenotypes, we apply different permutation strategies and investigate their effects on the outcomes.Genetics, Biostatisticsrf2283, tz33, shl5StatisticsArticlesLatent demographic profile estimation in hard-to-reach groups
http://academiccommons.columbia.edu/catalog/ac:184956
McCormick, Tyler H.; Zheng, Tianhttp://dx.doi.org/10.7916/D8F76BFQFri, 27 Mar 2015 00:00:00 +0000The sampling frame in most social science surveys excludes members of certain groups, known as hard-to-reach groups. These groups, or subpopulations, may be difficult to access (the homeless, e.g.), camouflaged by stigma (individuals with HIV/AIDS), or both (commercial sex workers). Even basic demographic information about these groups is typically unknown, especially in many developing nations. We present statistical models which leverage social network structure to estimate demographic characteristics of these subpopulations using Aggregated relational data (ARD), or questions of the form “How many X’s do you know?” Unlike other network-based techniques for reaching these groups, ARD require no special sampling strategy and are easily incorporated into standard surveys. ARD also do not require respondents to reveal their own group membership. We propose a Bayesian hierarchical model for estimating the demographic characteristics of hard-to-reach groups, or latent demographic profiles, using ARD. We propose two estimation techniques. First, we propose a Markov-chain Monte Carlo algorithm for existing data or cases where the full posterior distribution is of interest. For cases when new data can be collected, we propose guidelines and, based on these guidelines, propose a simple estimate motivated by a missing data approach. Using data from McCarty et al. [Human Organization 60 (2001) 28–39], we estimate the age and gender profiles of six hard-to-reach groups, such as individuals who have HIV, women who were raped, and homeless persons. We also evaluate our simple estimates using simulation studies.Statisticstz33StatisticsArticlesGenetic-linkage mapping of complex hereditary disorders to a whole-genome molecular-interaction network
http://academiccommons.columbia.edu/catalog/ac:184959
Iossifov, Ivan; Zheng, Tian; Baron, Miron; Gilliam, T. Conrad; Rzhetsky, Andreyhttp://dx.doi.org/10.7916/D85T3JD0Fri, 27 Mar 2015 00:00:00 +0000Common hereditary neurodevelopmental disorders such as autism, bipolar disorder, and schizophrenia are most likely both genetically multifactorial and heterogeneous. Because of these characteristics traditional methods for genetic analysis fail when applied to such diseases. To address the problem we propose a novel probabilistic framework that combines the standard genetic linkage formalism with whole-genome molecular-interaction data to predict pathways or networks of interacting genes that contribute to common heritable disorders. We apply the model to three large genotype–phenotype data sets, identify a small number of significant candidate genes for autism (24), bipolar disorder (21), and schizophrenia (25), and predict a number of gene targets likely to be shared among the disorders.Biostatistics, Geneticstz33StatisticsArticlesDiscovering influential variables: A method of partitions
http://academiccommons.columbia.edu/catalog/ac:184953
Chernoff, Herman; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8PR7TVMFri, 27 Mar 2015 00:00:00 +0000A trend in all scientific disciplines, based on advances in technology, is the increasing availability of high dimensional data in which are buried important information. A current urgent challenge to statisticians is to develop effective methods of finding the useful information from the vast amounts of messy and noisy data available, most of which are noninformative. This paper presents a general computer intensive approach, based on a method pioneered by Lo and Zheng for detecting which, of many potential explanatory variables, have an influence on a dependent variable Y. This approach is suited to detect influential variables, where causal effects depend on the confluence of values of several variables. It has the advantage of avoiding a difficult direct analysis, involving possibly thousands of variables, by dealing with many randomly selected small subsets from which smaller subsets are selected, guided by a measure of influence I. The main objective is to discover the influential variables, rather than to measure their effects. Once they are detected, the problem of dealing with a much smaller group of influential variables should be vulnerable to appropriate analysis. In a sense, we are confining our attention to locating a few needles in a haystack.Statistics, Computer scienceshl5, tz33StatisticsArticlesIdentification of gene interactions associated with disease from gene expression data using synergy networks
http://academiccommons.columbia.edu/catalog/ac:184938
Watkinson, John; Wang, Xiaodong; Zheng, Tian; Anastassiou, Dimitrishttp://dx.doi.org/10.7916/D81835DPFri, 27 Mar 2015 00:00:00 +0000Analysis of microarray data has been used for the inference of gene-gene interactions. If, however, the aim is the discovery of disease-related biological mechanisms, then the criterion for defining such interactions must be specifically linked to disease. Here we present a computational methodology that jointly analyzes two sets of microarray data, one in the presence and one in the absence of a disease, identifying gene pairs whose correlation with disease is due to cooperative, rather than independent, contributions of genes, using the recently developed information theoretic measure of synergy. High levels of synergy in gene pairs indicates possible membership of the two genes in a shared pathway and leads to a graphical representation of inferred gene-gene interactions associated with disease, in the form of a "synergy network." We apply this technique on a set of publicly available prostate cancer expression data and successfully validate our results, confirming that they cannot be due to pure chance and providing a biological explanation for gene pairs with exceptionally high synergy. Thus, synergy networks provide a computational methodology helpful for deriving "disease interactomes" from biological data. When coupled with additional biological knowledge, they can also be helpful for deciphering biological mechanisms responsible for disease.Genetics, Biostatisticsxw2008, tz33, da8Statistics, Electrical EngineeringArticlesOn Bootstrap Tests of Symmetry About an Unknown Median
http://academiccommons.columbia.edu/catalog/ac:184965
Zheng, Tian; Gastwirth, Joseph L.http://dx.doi.org/10.7916/D8X9296PFri, 27 Mar 2015 00:00:00 +0000It is important to examine the symmetry of an underlying distribution before applying some statistical procedures to a data set. For example, in the Zuni School District case, a formula originally developed by the Department of Education trimmed 5% of the data symmetrically from each end. The validity of this procedure was questioned at the hearing by Chief Justice Roberts. Most tests of symmetry (even nonparametric ones) are not distribution free in finite sample sizes. Hence, using asymptotic distribution may not yield an accurate type I error rate or/and loss of power in small samples. Bootstrap resampling from a symmetric empirical distribution function fitted to the data is proposed to improve the accuracy of the calculated p-value of several tests of symmetry. The results show that the bootstrap method is superior to previously used approaches relying on the asymptotic distribution of the tests that assumed the data come from a normal distribution. Incorporating the bootstrap estimate in a recently proposed test due to Miao, Gel and Gastwirth (2006) preserved its level and shows it has reasonable power properties on the family of distribution evaluated.Statisticstz33StatisticsArticlesProtecting Minorities in Large Binary Elections: A Test of Storable Votes Using Field Data
http://academiccommons.columbia.edu/catalog/ac:182487
Casella, Alessandra M.; Gelman, Andrew E.; Ehrenberg, Shuky; Shen, Jiehttp://dx.doi.org/10.7916/D8KH0M4QSun, 08 Feb 2015 00:00:00 +0000The legitimacy of democratic systems requires the protection of minority preferences while ideally treating every voter equally. During the 2006 student elections at Columbia University, we asked voters to rank the importance of different contests and to choose where to cast a single extra "bonus vote," had one been available — a simple version of Storable Votes. We then constructed distributions of intensities and electoral outcomes and estimated the probable impact of the bonus vote through bootstrapping techniques. The bonus vote performs well: when minority preferences are particularly intense, the minority wins at least one contest with 15-30 percent probability; when the minority wins, aggregate welfare increases with 85-95 percent probability. The paper makes two contributions: it tests the performance of storable votes in a setting where preferences were not controlled, and it suggests the use of bootstrapping techniques when appropriate replications of the data cannot be obtained.Political scienceac186, ag389Statistics, EconomicsArticlesSPAr package for Fan and Lo (2013) "A robust model-free approach for rare variants association studies incorporating gene-gene and gene-environmental interactions."
http://academiccommons.columbia.edu/catalog/ac:179424
Fan, Ruixue; Lo, Shaw-Hwahttp://dx.doi.org/10.7916/D84Q7SN6Fri, 07 Nov 2014 00:00:00 +0000Recently more and more evidence suggest that rare variants with much lower minor allele frequencies play significant roles in disease etiology. Advances in next-generation sequencing technologies will lead to many more rare variants association studies. Several statistical methods have been proposed to assess the effect of rare variants by aggregating information from multiple loci across a genetic region and testing the association between the phenotype and aggregated genotype. One limitation of existing methods is that they only look into the marginal effects of rare variants but do not systematically take into account effects due to interactions among rare variants and between rare variants and environmental factors. In this article, we propose the summation of partition approach (SPA), a robust model-free method that is designed specifically for detecting both marginal effects and effects due to gene-gene (G×G) and gene-environmental (G×E) interactions for rare variants association studies. SPA has three advantages. First, it accounts for the interaction information and gains considerable power in the presence of unknown and complicated G×G or G×E interactions. Secondly, it does not sacrifice the marginal detection power; in the situation when rare variants only have marginal effects it is comparable with the most competitive method in current literature. Thirdly, it is easy to extend and can incorporate more complex interactions; other practitioners and scientists can tailor the procedure to fit their own study friendly. Our simulation studies show that SPA is considerably more powerful than many existing methods in the presence of G×G and G×E interactions. This package is also maintained on the Comprehensive R Archive Network (http://cran.r-project.org). It contains the R programs, user's manual and example codes.Genetics, Statisticsrf2283, shl5StatisticsComputer softwareSource codes for GLMLE algorithm
http://academiccommons.columbia.edu/catalog/ac:178966
He, Ranhttp://dx.doi.org/10.7916/D8HH6HQRFri, 24 Oct 2014 00:00:00 +0000These are the R source codes for the algorithm proposed for fitting exponential random graph models (ERGMs) on large social networks in our paper "Estimation of exponential random graph models for large social networks via graph limits". Specifically, the ERGM model we implement is the one that consider homomorphism densities of edges, two-stars and triangles, the one we examine in the above paper.Statistics, Computer sciencerh2528StatisticsComputer softwareMathematical Modeling of Insider Trading
http://academiccommons.columbia.edu/catalog/ac:178871
Bilina Falafala, Roselinehttp://dx.doi.org/10.7916/D89W0D33Mon, 13 Oct 2014 00:00:00 +0000In this thesis, we study insider trading and consider a financial market and an enlarged financial market whose sets of information are respectively represented by the filtrations F and G. The filtration G is obtained by initially expanding the filtration F. We also consider that we have a finite trading horizon. First, we show that under certain conditions the enlarged market satisfies no free lunch with vanishing risk (NFLVR) locally and therefore satisfies no arbitrage with respect to admissible simple predictable trading strategies. In addition, we generalize the structure of all the G local martingale deflators and find sufficient conditions under which the enlarged market satisfies NFLVR. We apply our results to some recent examples of insider trading that have appeared in newspapers and by doing so, show the limitations of some previous works that have studied the stability of the NFLVR property under an initial expansion. \newline Second, assuming the enlarged market satisfies NFLVR and markets are incomplete, we define a notion of risk and compare the risk of a market or liquidity trader to the risk of an insider trader. We prove that the risk of an insider is smaller than the risk of a market/liquidity trader under some sufficient conditions that involve their respective trading strategies. We find a relationship between the trading strategies of a market trader and of an insider when the risk neutral measure of the market is used. If an insider trades using the market risk neutral measure and not her own, then her trading strategy should involve not only the stock but also the volatility of the stock. \newline Finally, assuming that the enlarged market satisfies NFLVR locally, we provide a way for an insider to price her financial claims. We also define a new type of process that we call a quasi-local martingale and prove that the stock price process under local NFLVR is one such process.Applied mathematics, FinanceStatisticsDissertationsApplying Large-Scale Data and Modern Statistical Methods to Classical Problems in American Politics
http://academiccommons.columbia.edu/catalog/ac:177212
Ghitza, Yairhttp://dx.doi.org/10.7916/D8ZS2TT3Mon, 08 Sep 2014 00:00:00 +0000Exponential growth in data storage and computing capacity, alongside the development of new statistical methods, have facilitated powerful and flexible new research capabilities across a variety of disciplines. In each of these three essays, I use some new large-scale data source or advanced statistical method to address a well-known problem in the American Political Science literature. In the first essay, I build a generational model of presidential voting, in which long-term partisan presidential voting preferences are formed, in large part, through a weighted "running tally" of retrospective presidential evaluations, where weights are determined by the age in which the evaluation was made. By gathering hundreds of thousands of survey responses in combination with a new Bayesian model, I show that the political events of a voter's teenage and early adult years, centered around the age of 18, are enormously influential, particularly among white voters. In the second and third essays, I leverage a national voter registration database, which contains records for over 190 million registered voters, alongside methods like multilevel regression and poststratification (MRP) and coarsened exact matching (CEM) to address critical issues in public opinion research and in our understanding of the consequences of higher or lower turnout. In the process, I make numerous methodological and substantive contributions, including: building on the capabilities of MRP generally, describing methods for dealing with data of this size in the context of social science research, and characterizing mathematical limits of how turnout can impact election outcomes.Political scienceyg2173Political Science, StatisticsDissertationsRheumatoid arthritis-associated gene-gene interaction network for rheumatoid arthritis candidate genes
http://academiccommons.columbia.edu/catalog/ac:184531
Huang, Chien-Hsun; Cong, Lei; Xie, Jun; Qiao, Bo; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8HX1B3VMon, 08 Sep 2014 00:00:00 +0000Rheumatoid arthritis (RA, MIM 180300) is a chronic and complex autoimmune disease. Using the North American Rheumatoid Arthritis Consortium (NARAC) data set provided in Genetic Analysis Workshop 16 (GAW16), we used the genotype-trait distortion (GTD) scores and proposed analysis procedures to capture the gene-gene interaction effects of multiple susceptibility gene regions on RA. In this paper, we focused on 27 RA candidate gene regions (531 SNPs) based on a literature search. Statistical significance was evaluated using 1000 permutations. HLADRB1 was found to have strong marginal association with RA. We identified 14 significant interactions (p < 0.01), which were aggregated into an association network among 12 selected candidate genes PADI4, FCGR3, TNFRSF1B, ITGAV, BTLA, SLC22A4, IL3, VEGF, TNF, NFKBIL1, TRAF1-C5, and MIF. Based on our and other contributors' findings during the GAW16 conference, we further studied 24 candidate regions with 336 SNPs. We found 23 significant interactions (p-value < 0.01), nine interactions in addition to our initial findings, and the association network was extended to include candidate genes HLA-A, HLA-B, HLA-C, CTLA4, and IL6. As we will discuss in this paper, the reported possible interactions between genes may suggest potential biological activities of RA.Biostatistics, Geneticsshl5, tz33StatisticsArticlesGenome-wide gene-based analysis of rheumatoid arthritis-associated interaction with PTPN22 and HLA-DRB1
http://academiccommons.columbia.edu/catalog/ac:184526
Qiao, Bo; Huang, Chien Hsun; Chong, Lei; Xie, Jun; Lo, Shaw-Hwa; Zheng, Tianhttp://dx.doi.org/10.7916/D8NP22VMMon, 08 Sep 2014 00:00:00 +0000The genes PTPN22 and HLA-DRB1 have been found by a number of studies to confer an increased risk for rheumatoid arthritis (RA), which indicates that both genes play an important role in RA etiology. It is believed that they not only have strong association with RA individually, but also interact with other related genes that have not been found to have predisposing RA mutations. In this paper, we conduct genome-wide searches for RA-associated gene-gene interactions that involve PTPN22 or HLA-DRB1 using the Genetic Analysis Workshop 16 Problem 1 data from the North American Rheumatoid Arthritis Consortium. MGC13017, HSPCAL3, MIA, PTPNS1L, and IGLVI-70, which showed association with RA in previous studies, have been confirmed in our analysis.Genetics, Biostatisticsshi5, tz33StatisticsArticlesUnbiased Penetrance Estimates with Unknown Ascertainment Strategies
http://academiccommons.columbia.edu/catalog/ac:175879
Gore, Kristenhttp://dx.doi.org/10.7916/D8KP8098Mon, 07 Jul 2014 00:00:00 +0000Allelic variation in the genome leads to variation in individuals' production of proteins. This, in turn, leads to variation in traits and development, and, in some cases, to diseases. Understanding the genetic basis for disease can aid in the search for therapies and in guiding genetic counseling. Thus, it is of interest to discover the genes with mutations responsible for diseases and to understand the impact of allelic variation at those genes. A subject's genetic composition is commonly referred to as the subject's genotype. Subjects who carry the gene mutation of interests are referred to as carriers. Subjects who are afflicted with a disease under study (that is, subjects who exhibit the phenotype) are termed affected carriers. The age-specific probability that a given subject will exhibit a phenotype of interest, given mutation status at a gene is known as penetrance. Understanding penetrance is an important facet of genetic epidemiology. Penetrance estimates are typically calculated via maximum likelihood from family data. However, penetrance estimates can be biased if the nature of the sampling strategy is not correctly reflected in the likelihood. Unfortunately, sampling of family data may be conducted in a haphazard fashion or, even if conducted systematically, might be reported in an incomplete fashion. Bias is possible in applying likelihood methods to reported data if (as is commonly the case) some unaffected family members are not represented in the reports. The purpose here is to present an approach to find efficient and unbiased penetrance estimates in cases where there is incomplete knowledge of the sampling strategy and incomplete information on the full pedigree structure of families included in the data. The method may be applied with different conjectural assumptions about the ascertainment strategy to balance the possibly biasing effects of wishful assumptions about the sampling strategy with the efficiency gains that could be obtained through valid assumptions.StatisticsStatisticsDissertationsStatistical Inference and Experimental Design for Q-matrix Based Cognitive Diagnosis Models
http://academiccommons.columbia.edu/catalog/ac:176169
Zhang, Stephaniehttp://dx.doi.org/10.7916/D8TQ5ZP5Mon, 07 Jul 2014 00:00:00 +0000There has been growing interest in recent years in using cognitive diagnosis models for diagnostic measurement, i.e., classification according to multiple discrete latent traits. The Q-matrix, an incidence matrix specifying the presence or absence of a relationship between each item in the assessment and each latent attribute, is central to many of these models. Important applications include educational and psychological testing; demand in education, for example, has been driven by recent focus on skills-based evaluation. However, compared to more traditional models coming from classical test theory and item response theory, cognitive diagnosis models are relatively undeveloped and suffer from several issues limiting their applicability. This thesis exams several issues related to statistical inference and experimental design for Q-matrix based cognitive diagnosis models. We begin by considering one of the main statistical issues affecting the practical use of Q-matrix based cognitive diagnosis models, the identifiability issue. In statistical models, identifiability is prerequisite for most common statistical inferences, including parameter estimation and hypothesis testing. With Q-matrix based cognitive diagnosis models, identifiability also affects the classification of respondents according to their latent traits. We begin by examining the identifiability of model parameters, presenting necessary and sufficient conditions for identifiability in several settings. Depending on the area of application and the researcher's degree of control over the experiment design, fulfilling these identifiability conditions may be difficult. The second part of this thesis proposes new methods for parameter estimation and respondent classification for use with non-identifiable models. In addition, our framework allows consistent estimation of the severity of the non-identifiability problem, in terms of the proportion of the population affected by it. The implications of this measure for the design of diagnostic assessments are also discussed.Statistics, Educational tests and measurements, Quantitative psychology and psychometricsStatisticsDissertationsToward Reproducible Computational Research: An Empirical Analysis of Data and Code Policy Adoption by Journals
http://academiccommons.columbia.edu/catalog/ac:174140
Stodden, Victoria C.; Guo, Peixuan; Ma, Zhaokunhttp://dx.doi.org/10.7916/D80K26NNWed, 21 May 2014 00:00:00 +0000Journal policy on research data and code availability is an important part of the ongoing shift toward publishing reproducible computational science. This article extends the literature by studying journal data sharing policies by year (for both 2011 and 2012) for a referent set of 170 journals. We make a further contribution by evaluating code sharing policies, supplemental materials policies, and open access status for these 170 journals for each of 2011 and 2012. We build a predictive model of open data and code policy adoption as a function of impact factor and publisher and find higher impact journals more likely to have open data and code policies and scientific societies more likely to have open data and code policies than commercial publishers. We also find open data policies tend to lead open code policies, and we find no relationship between open data and code policies and either supplemental material policies or open access journal status. Of the journals in this study, 38% had a data policy, 22% had a code policy, and 66% had a supplemental materials policy as of June 2012. This reflects a striking one year increase of 16% in the number of data policies, a 30% increase in code policies, and a 7% increase in the number of supplemental materials policies. We introduce a new dataset to the community that categorizes data and code sharing, supplemental materials, and open access policies in 2011 and 2012 for these 170 journals.Technical communication, Information sciencevcs2115, zm2168StatisticsArticlesA Characterization of Markov Equivalence Classes for Acyclic Digraphs
http://academiccommons.columbia.edu/catalog/ac:173896
Andersson, Steen A.; Madigan, David B.; Perlman, Michael D.http://dx.doi.org/10.7916/D8FX77J3Thu, 15 May 2014 00:00:00 +0000Undirected graphs and acyclic digraphs (ADG's), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multiviarate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. Whereas the undirected graph associated with a dependence model is uniquely determined, there may be many ADG's that determine the same dependence (i.e., Markov) model. Thus, the family of all ADG's with a given set of vertices is naturally partitioned into Markov-equivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection of model averaging, that fail to take into account these equivalence classes may incur substantial computational or other inefficiences. Here it is show that each Markov-equivalence class is uniquely determined by a single chain graph, the essential graph, that is itself simultaneously Markov equivalent to all ADG's in the equivalence class. Essential graphs are characterized, a polynomial-time algorithm for their construction is given, and their applications to model selection and other statistical questions are described.Mathematics, Statistics, Theoretical mathematicsdm2418StatisticsArticlesMedication-Wide Association Studies
http://academiccommons.columbia.edu/catalog/ac:173912
Ryan, P. B.; Stang, P. E.; Madigan, David B.; Schuemie, M. J.; Hripcsak, George M.http://dx.doi.org/10.7916/D8PG1PVXThu, 15 May 2014 00:00:00 +0000Undiscovered side effects of drugs can have a profound effect on the health of the nation, and electronic health-care databases offer opportunities to speed up the discovery of these side effects. We applied a “medication-wide association study” approach that combined multivariate analysis with exploratory visualization to study four health outcomes of interest in an administrative claims database of 46 million patients and a clinical database of 11 million patients. The technique had good predictive value, but there was no threshold high enough to eliminate false-positive findings. The visualization not only highlighted the class effects that strengthened the review of specific products but also underscored the challenges in confounding. These findings suggest that observational databases are useful for identifying potential associations that warrant further consideration but are unlikely to provide definitive evidence of causal effects.Pharmacology, Statistics, Bioinformaticsdm2418, gh13Statistics, Biomedical InformaticsArticlesLearning Theory Analysis for Association Rules and Sequential Event Prediction
http://academiccommons.columbia.edu/catalog/ac:173905
Rudin, Cynthia; Letham, Benjamin; Madigan, David B.http://dx.doi.org/10.7916/D82N50C1Thu, 15 May 2014 00:00:00 +0000We present a theoretical analysis for prediction algorithms based on association rules. As part of this analysis, we introduce a problem for which rules are particularly natural, called “sequential event prediction." In sequential event prediction, events in a sequence are revealed one by one, and the goal is to determine which event will next be revealed. The training set is a collection of past sequences of events. An example application is to predict which item will next be placed into a customer's online shopping cart, given his/her past purchases. In the context of this problem, algorithms based on association rules have distinct advantages over classical statistical and machine learning methods: they look at correlations based on subsets of co-occurring past events (items a and b imply item c), they can be applied to the sequential event prediction problem in a natural way, they can potentially handle the “cold start" problem where the training set is small, and they yield interpretable predictions. In this work, we present two algorithms that incorporate association rules. These algorithms can be used both for sequential event prediction and for supervised classification, and they are simple enough that they can possibly be understood by users, customers, patients, managers, etc. We provide generalization guarantees on these algorithms based on algorithmic stability analysis from statistical learning theory. We include a discussion of the strict minimum support threshold often used in association rule mining, and introduce an “adjusted confidence" measure that provides a weaker minimum support condition that has advantages over the strict minimum support. The paper brings together ideas from statistical learning theory, association rule mining and Bayesian analysis.Statistics, Artificial intelligencedm2418StatisticsArticlesBook Reviews: Principles of Data Mining. By David Hand, Heikki Mannila, and Padhraic Smyth.
http://academiccommons.columbia.edu/catalog/ac:173915
Madigan, David B.http://dx.doi.org/10.7916/D8DZ06D8Thu, 15 May 2014 00:00:00 +0000"Principles of Data Mining. By David Hand, Heikki Mannila, and Padhraic Smyth. MIT Press, Cambridge, MA, 2001. $50.00. xxxii+546 pp., hardcover. ISBN 0-262-08290-X. Is data mining the same as statistics? The distinguished authors of Principles of Data Mining struggle to make a distinction between the two subjects. In the end, what they have written is a fine applied statistics text." -- page 501Statisticsdm2418StatisticsReviewsAnalysis of Variance of Cross-Validation Estimators of the Generalization Error
http://academiccommons.columbia.edu/catalog/ac:173902
Markatou, Marianthi; Tian, Hong; Biswas, Shameek; Hripcsak, George M.http://dx.doi.org/10.7916/D86D5R2XThu, 15 May 2014 00:00:00 +0000This paper brings together methods from two different disciplines: statistics and machine learning. We address the problem of estimating the variance of cross-validation (CV) estimators of the generalization error. In particular, we approach the problem of variance estimation of the CV estimators of generalization error as a problem in approximating the moments of a statistic. The approximation illustrates the role of training and test sets in the performance of the algorithm. It provides a unifying approach to evaluation of various methods used in obtaining training and test sets and it takes into account the variability due to different training and test sets. For the simple problem of predicting the sample mean and in the case of smooth loss functions, we show that the variance of the CV estimator of the generalization error is a function of the moments of the random variables Y=Card(Sj ∩ Sj') and Y*=Card(Sjc ∩ Sj'c), where Sj, Sj' are two training sets, and Sjc, Sj'c are the corresponding test sets. We prove that the distribution of Y and Y* is hypergeometric and we compare our estimator with the one proposed by Nadeau and Bengio (2003). We extend these results in the regression case and the case of absolute error loss, and indicate how the methods can be extended to the classification case. We illustrate the results through simulation.Statistics, Artificial intelligencemm168, ht2031, spb2003, gh13Statistics, Biomedical Informatics, BiostatisticsArticlesAlgorithms for Sparse Linear Classifiers in the Massive Data Setting
http://academiccommons.columbia.edu/catalog/ac:173908
Balakrishnan, Suhrid; Bartlett, Peter; Madigan, David B.http://dx.doi.org/10.7916/D8Z0368XThu, 15 May 2014 00:00:00 +0000Classifiers favoring sparse solutions, such as support vector machines, relevance vector machines, LASSO-regression based classifiers, etc., provide competitive methods for classification problems in high dimensions. However, current algorithms for training sparse classifiers typically scale quite unfavorably with respect to the number of training examples. This paper proposes online and multi-pass algorithms for training sparse linear classifiers for high dimensional data. These algorithms have computational complexity and memory requirements that make learning on massive data sets feasible. The central idea that makes this possible is a straightforward quadratic approximation to the likelihood function.Statistics, Artificial intelligencedm2418StatisticsArticlesA One-Pass Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets
http://academiccommons.columbia.edu/catalog/ac:173899
Balakrishnan, Suhrid; Madigan, David B.http://dx.doi.org/10.7916/D8B56GTPThu, 15 May 2014 00:00:00 +0000For Bayesian analysis of massive data, Markov chain Monte Carlo (MCMC) techniques often prove infeasible due to computational resource constraints. Standard MCMC methods generally require a complete scan of the dataset for each iteration. Ridgeway and Madigan (2002) and Chopin (2002b) recently presented importance sampling algorithms that combined simulations from a posterior distribution conditioned on a small portion of the dataset with a reweighting of those simulations to condition on the remainder of the dataset. While these algorithms drastically reduce the number of data accesses as compared to traditional MCMC, they still require substantially more than a single pass over the dataset. In this paper, we present "1PFS," an efficient, one-pass algorithm. The algorithm employs a simple modification of the Ridgeway and Madigan (2002) particle filtering algorithm that replaces the MCMC based "rejuvenation" step with a more efficient "shrinkage" kernel smoothing based step. To show proof-of-concept and to enable a direct comparison, we demonstrate 1PFS on the same examples presented in Ridgeway and Madigan (2002), namely a mixture model for Markov chains and Bayesian logistic regression. Our results indicate the proposed scheme delivers accurate parameter estimates while employing only a single pass through the data.Mathematics, Statisticsdm2418StatisticsArticlesBayesian Hierarchical Rule Modeling for Predicting Medical Conditions
http://academiccommons.columbia.edu/catalog/ac:173882
McCormick, Tyler H.; Rudin, Cynthia; Madigan, David B.http://dx.doi.org/10.7916/D8V69GP1Wed, 14 May 2014 00:00:00 +0000We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future medical conditions given the patient’s current and past history of reported conditions. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “condition 1 and condition 2 → condition 3”) from a large set of candidate rules. Because this method “borrows strength” using the conditions of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of conditions is available.Applied mathematics, Statistics, Medicinedm2418StatisticsArticlesCorrection: Separation and completeness properties for AMP chain graph Markov models
http://academiccommons.columbia.edu/catalog/ac:173887
Madigan, David B.; Levitz, Michael; Perlman, Michael D.http://dx.doi.org/10.7916/D8QF8R05Wed, 14 May 2014 00:00:00 +0000Correction of table 2 on page 1757 of 'Separation and completeness properties for AMP chain graph Markov models', Annals of Statistics, volume 29 (2001).Mathematics, Statisticsdm2418StatisticsArticlesGenerating Productive Dialogue between Consulting Statisticians and their Clients in the Pharmaceutical and Medical Research Settings
http://academiccommons.columbia.edu/catalog/ac:173832
Emir, Birol; Amaratunga, Dhammika; Beltangady, Mohan; Cabrera, Javier; Freeman, Roy; Madigan, David B.; Nguyen, Ha H.; Whalen, Edward Patrickhttp://dx.doi.org/10.7916/D8PK0D8NTue, 13 May 2014 00:00:00 +0000Due to the ever-increasing complexity of scientific technologies and resulting data, consulting statisticians are becoming more involved in the design, conduct, and analysis of biomedical research. This requires extensive collaboration between the consulting statistician and nonstatisticians, such as researchers, clinicians, and corporate executives. Consequently, a successful consulting career is becoming ever more dependent on the statistician's ability to effectively communicate with nonstatisticians. This is especially true when more complex, nontraditional analytical methods are required. In this paper, we examine the collaboration between statisticians and nonstatisticians from three different professional perspectives. Integrating these perspectives, we discuss ways to help the consulting statistician generate productive dialogue with clients. Finally, we examine how universities can better prepare students for careers in statistical consulting by incorporating more communication-based elements into their curriculum and by offering students ample opportunities to collaborate with nonstatisticians. Overall, we designed this exercise to help the consulting statistician generate dialogue with clients that results in more productive collaborations and a more satisfying work experience.Statistics, Bioinformatics, Medicinebe2166, dm2418, hhn2108, ew2320StatisticsArticlesLocation Estimation in Wireless Networks: A Bayesian Approach
http://academiccommons.columbia.edu/catalog/ac:173820
Madigan, David B.; Ju, Wen-Hua; Krishnan, P.; Krishnakumar, A. S. ; Zorych, Ivanhttp://dx.doi.org/10.7916/D82V2D74Tue, 13 May 2014 00:00:00 +0000We present a Bayesian hierarchical model for indoor location estimation in wireless networks. We demonstrate that out model achieves accuracy that is similar to other published models and algorithms. By harnessing prior knowledge, our model drastically reduces the requirement for training data as compared with existing approaches.Mathematics, Statistics, Applied mathematicsdm2418StatisticsArticlesA Flexible Bayesian Generalized Linear Model for Dichotomous Response Data with an Application to Text Categorization
http://academiccommons.columbia.edu/catalog/ac:173817
Eyheramendy, Susana; Madigan, David B.http://dx.doi.org/10.7916/D86M34ZFTue, 13 May 2014 00:00:00 +0000We present a class of sparse generalized linear models that include probit and logistic regression as special cases and offer some extra flexibility. We provide an EM algorithm for learning the parameters of these models from data. We apply our method in text classification and in simulated data and show that our method outperforms the logistic and probit models and also the elastic net, in general by a substantial margin.Mathematics, Statistics, Theoretical mathematicsdm2418StatisticsBook chaptersBayesian Model Averaging: a Tutorial (with Comments by M. Clyde, David Draper and E. I. George, and a Rejoinder by the Authors)
http://academiccommons.columbia.edu/catalog/ac:173853
Hoeting, Jennifer A.; Madigan, David B.; Raftery, Adrian E.; Volinsky, Chris T.; Clyde, M.; Draper, David; George, E. I.http://dx.doi.org/10.7916/D84M92N7Tue, 13 May 2014 00:00:00 +0000Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA)provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples.In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software.Statisticsdm2418StatisticsArticlesA Hierarchical Model for Association Rule Mining of Sequential Events: An Approach to Automated Medical Symptom Prediction
http://academiccommons.columbia.edu/catalog/ac:173838
McCormick, Tyler H.; Rudin, Cynthia; Madigan, David B.http://dx.doi.org/10.7916/D89C6VJDTue, 13 May 2014 00:00:00 +0000In many healthcare settings, patients visit healthcare professionals periodically and report multiple medical conditions, or symptoms, at each encounter. We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future symptoms given the patient’s current and past history of reported symptoms. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “symptom 1 and symptom 2 → symptom 3 ”) from a large set of candidate rules. Because this method “borrows strength” using the symptoms of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of symptoms is available.Mathematics, Statistics, Medicinedm2418StatisticsArticles[Least Angle Regression]: Discussion
http://academiccommons.columbia.edu/catalog/ac:173841
Madigan, David B.; Ridgeway, Greghttp://dx.doi.org/10.7916/D81V5C29Tue, 13 May 2014 00:00:00 +0000Algorithms for simultaneous shrinkage and selection in regression and classification provide attractive solutions to knotty old statistical challenges. Nevertheless, as far as we can tell, Tibshirani's Lasso algorithm has had little impact on statistical practice. Two particular reasons for this may be the relative inefficiency of the original Lasso algorithm and the relative complexity of more recent Lasso algorithms [e.g., Osborne, Presnell and Turlach (2000)]. Efron, Hastie, Johnstone and Tibshirani have provided an efficient, simple algorithm for the Lasso as well as algorithms for stagewise regression and the new least angle regression. As such this paper is an important contribution to statistical computing.Mathematics, Statisticsdm2418StatisticsArticles[A Report on the Future of Statistics]: Comment
http://academiccommons.columbia.edu/catalog/ac:173850
Madigan, David B.; Stuetzle, Wernerhttp://dx.doi.org/10.7916/D8D50K3VTue, 13 May 2014 00:00:00 +0000"Extraordinary opportunities for statistical ideas and for statisticians now present themselves. However, to take advantage of the opportunities, statistics has to change the way in which it recruits and trains students. Statistics has primarily focused on squeezing the maximum amount of information out of limited data. This paradigm is rapidly diminishing in importance and statistics education finds itself out of step with reality. The problems begin at the high school and undergraduate levels, where the standard course includes a narrow set of pre-computing-era topics. At the graduate level, the typical statistics program suffers from the same problem..." -- page 408Mathematics education, Higher educationdm2418StatisticsArticlesA Note on Equivalence Classes of Directed Acyclic Independence Graphs
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Madigan, David B.http://dx.doi.org/10.7916/D8TB150CTue, 13 May 2014 00:00:00 +0000Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.Mathematics, Statisticsdm2418StatisticsArticles[Bayesian Analysis in Expert Systems]: Comment: What's Next?
http://academiccommons.columbia.edu/catalog/ac:173856
Madigan, David B.http://dx.doi.org/10.7916/D8W37TFJTue, 13 May 2014 00:00:00 +0000"These papers represent two of the many different graphical modeling camps that have emerged from a flurry of activity in the past decade. The paper by Cox and Wermuth falls within the statistical graphical modeling camp and provides a useful generalization of that body of work. There is, of course, a price to be paid for this generality, namely that the interpretation of the graphs is more complex...The paper by Spiegelhalter, Dawid, Lauritzen and Cowell falls within the probabilistic expert system camp. This is a tour de force by researchers responsible for much of the astonishing progress in this area. Ten years ago, probabilistic models were shunned by the artificial intelligence community. That they are now widely accepted and used is due in large measure to the insights and efforts of these authors, along with other pioneers such as Judea Pearl and Peter Cheeseman..." -- page 261Mathematics, Statisticsdm2418StatisticsArticlesSeparation and Completeness Properties for Amp Chain Graph Markov Models
http://academiccommons.columbia.edu/catalog/ac:173847
Levitz, Michael; Perlman, Michael D.; Madigan, David B.http://dx.doi.org/10.7916/D8X34VJGTue, 13 May 2014 00:00:00 +0000Pearl’s well-known d-separation criterion for an acyclic directed graph (ADG) is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relations in the Markov model determined by the graph. This paper introduces p-separation, a pathwise separation criterion that efficiently identifies all valid conditional independences under the Andersson–Madigan–Perlman (AMP) alternative Markov property for chain graphs (= adicyclic graphs), which include both ADGs and undirected graphs as special cases. The equivalence of p-separation to the augmentation criterion occurring in the AMP global Markov property is established, and p-separation is applied to prove completeness of the global Markov property for AMP chain graph models. Strong completeness of the AMP Markov property is established, that is, the existence of Markov perfect distributions that satisfy those and only those conditional independences implied by the AMP property(equivalently, by p-separation). A linear-time algorithm for determining p-separation is presented.Mathematics, Statistics, Theoretical mathematicsdm2418StatisticsArticlesFit GFuseTLP penalized conditional logistic regression model for high-dimensional one-to- one matched case-control data
http://academiccommons.columbia.edu/catalog/ac:174087
Zhou, Hui; Wang, Shuang; Zheng, Tianhttp://dx.doi.org/10.7916/D8028PNJMon, 12 May 2014 00:00:00 +0000Fit GFuseTLP penalized conditional logistic regression model for high-dimensional one-to- one matched case-control dataStatisticshz2240, sw2206, tz33Statistics, BiostatisticsComputer softwareA Point Process Model for the Dynamics of Limit Order Books
http://academiccommons.columbia.edu/catalog/ac:171221
Vinkovskaya, Ekaterinahttp://dx.doi.org/10.7916/D88913WWFri, 28 Feb 2014 00:00:00 +0000This thesis focuses on the statistical modeling of the dynamics of limit order books in electronic equity markets. The statistical properties of events affecting a limit order book -market orders, limit orders and cancellations- reveal strong evidence of clustering in time, cross-correlation across event types and dependence of the order flow on the bid-ask spread. Further investigation reveals the presence of a self-exciting property - that a large number of events in a given time period tends to imply a higher probability of observing a large number of events in the following time period. We show that these properties may be adequately represented by a multivariate self-exciting point process with multiple regimes that reflect changes in the bid-ask spread. We propose a tractable parametrization of the model and perform a Maximum Likelihood Estimation of the model using high-frequency data from the Trades and Quotes database for US stocks. We show that the model may be used to obtain predictions of order flow and that its predictive performance beats the Poisson model as well as Moving Average and Auto Regressive time series models.StatisticsStatisticsDissertationsMixed Methods for Mixed Models
http://academiccommons.columbia.edu/catalog/ac:169644
Dorie, Vincent J.http://dx.doi.org/10.7916/D8V40S5XWed, 22 Jan 2014 00:00:00 +0000This work bridges the frequentist and Bayesian approaches to mixed models by borrowing the best features from both camps: point estimation procedures are combined with priors to obtain accurate, fast inference while posterior simulation techniques are developed that approximate the likelihood with great precision for the purposes of assessing uncertainty. These allow flexible inferences without the need to rely on expensive Markov chain Monte Carlo simulation techniques. Default priors are developed and evaluated in a variety of simulation and real-world settings with the end result that we propose a new set of standard approaches that yield superior performance at little computational cost.StatisticsStatisticsDissertationsKernel-based association measures
http://academiccommons.columbia.edu/catalog/ac:167034
Liu, Yinghttp://hdl.handle.net/10022/AC:P:22154Thu, 07 Nov 2013 00:00:00 +0000Measures of associations have been widely used for describing the statistical relationships between two sets of variables. Traditional association measures tend to focus on specialized settings (specific types of variables or association patterns). Based on an in-depth summary of existing measures, we propose a general framework for association measures unifying existing methods and novel extensions based on kernels, including practical solutions to computational challenges. The proposed framework provides improved feature selection and extensions to a variety of current classifiers. Specifically, we introduce association screening and variable selection via maximizing kernel-based association measures. We also develop a backward dropping procedure for feature selection when there are a large number of candidate variables. We evaluate our framework using a wide variety of both simulated and real data. In particular, we conduct independence tests and feature selection using kernel association measures on diversified association patterns of different dimensions and variable types. The results show the superiority of our methods to existing ones. We also apply our framework to four real-word problems, three from statistical genetics and one of gender prediction from handwriting. We demonstrate through these applications both the de novo construction of new kernels and the adaptation of existing kernels tailored to the data at hand, and how kernel-based measures of associations can be naturally applied to different data structures including functional input and output spaces. This shows that our framework can be applied to a wide range of real world problems and work well in practice.Statistics, Computer scienceyl2802StatisticsDissertationsInference of functional neural connectivity and convergence acceleration methods
http://academiccommons.columbia.edu/catalog/ac:179409
Nikitchenko, Maxim V.http://hdl.handle.net/10022/AC:P:22052Thu, 31 Oct 2013 00:00:00 +0000The knowledge of the maps of neuronal interactions is key for system neuroscience, but at the moment we possess relatively little of it . The recent development of experimental methods which allow a simultaneous recording of the spiking activity, but not the intracellular voltage, of thousands of neurons gives us an opportunity to start filling that gap. In Chapter 2, I present a method for the inference of the parameters of the leaky integrate-and-fire (LIF) model featuring time-dependent currents and conductances based only on the extracellular recording of spiking in the network. The fitted parameters can describe the functional connections in the network, as well as the internal properties of the cells. The method can also be used to determine whether a single-compartment model of a neuron should include conductance- or current-based synapses, or their mixture. In addition, because the same mathematical model describes some of the flavors of the Drift Diffusion Model (DDM), popular in the studies of decision making process, the presented method can be readily used to fit their parameters. Making the proposed inference procedure -- based on the expectation-maximization (EM) algorithm -- accurate and robust, necessitated a development of a new numerical adaptive-grid (AG) method for the forward-backward (FB) propagation of the probability density, which is required in the computation of the sufficient statistic in the EM algorithm. These topics are covered in Chapter 3. Another issue which had to be addressed in order to obtain a usable inference algorithm is the well known slow convergence of the EM algorithm in the flat regions of the loglikelihood. Two complementary approaches to this issue are presented in this dissertation. In Chapter 4, I present a new framework for the acceleration of convergence of iterative algorithms (not limited to the EM) which unifies all previously known methods and allows us to construct a new method demonstrating the best performance of them all. To make the computations even faster, I wrote a Matlab package which allows them to be done in parallel on several machines and clusters. As one can see, all the aforementioned projects were sprouted up from one "head" project on the inference of the LIF model parameters. At the end of the dissertation, I briefly describe a disconnected project which is devoted to the development of a flexible experimental setup (software and hardware) for behavioral experiments, with a specific application to a particular type of the virtual Morris water maze experiment (VMWM).Neurosciences, Statisticsmvn2104Statistics, Neurobiology and BehaviorDissertationsLow-rank graphical models and Bayesian inference in the statistical analysis of noisy neural data
http://academiccommons.columbia.edu/catalog/ac:166472
Smith, Carl Alexanderhttp://hdl.handle.net/10022/AC:P:21991Fri, 11 Oct 2013 00:00:00 +0000We develop new methods of Bayesian inference, largely in the context of analysis of neuroscience data. The work is broken into several parts. In the first part, we introduce a novel class of joint probability distributions in which exact inference is tractable. Previously it has been difficult to find general constructions for models in which efficient exact inference is possible, outside of certain classical cases. We identify a class of such models that are tractable owing to a certain "low-rank" structure in the potentials that couple neighboring variables. In the second part we develop methods to quantify and measure information loss in analysis of neuronal spike train data due to two types of noise, making use of the ideas developed in the first part. Information about neuronal identity or temporal resolution may be lost during spike detection and sorting, or precision of spike times may be corrupted by various effects. We quantify the information lost due to these effects for the relatively simple but sufficiently broad class of Markovian model neurons. We find that decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments. We also apply the ideas of the low-rank models from the first section to defining a class of prior distributions over the space of stimuli (or other covariate) which, by conjugacy, preserve the tractability of inference. In the third part, we treat Bayesian methods for the estimation of sparse signals, with application to the locating of synapses in a dendritic tree. We develop a compartmentalized model of the dendritic tree. Building on previous work that applied and generalized ideas of least angle regression to obtain a fast Bayesian solution to the resulting estimation problem, we describe two other approaches to the same problem, one employing a horseshoe prior and the other using various spike-and-slab priors. In the last part, we revisit the low-rank models of the first section and apply them to the problem of inferring orientation selectivity maps from noisy observations of orientation preference. The relevant low-rank model exploits the self-conjugacy of the von Mises distribution on the circle. Because the orientation map model is loopy, we cannot do exact inference on the low-rank model by the forward backward algorithm, but block-wise Gibbs sampling by the forward backward algorithm speeds mixing. We explore another von Mises coupling potential Gibbs sampler that proves to effectively smooth noisily observed orientation maps.Statistics, Neurosciencescas2207Statistics, ChemistryDissertationsThe Challenge of Communicating Computational Research
http://academiccommons.columbia.edu/catalog/ac:165636
Hong, Neil Chue; Jockers, Matthew L.; Ellis, Daniel P. W.; Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:21703Fri, 20 Sep 2013 00:00:00 +0000Computational approaches to scholarship have revolutionized how research is done but have at the same time complicated the process of disseminating the results of that research. Conclusions may be produced using mathematical models or custom software that are not easily accessible to, or reproducible by, those outside the research team. And in some fields, a lack of understanding of computational approaches may lead to skepticism about their use. The panel considers urgent questions faced by researchers across the range of academic disciplines. How can scientists and social scientists address the lack of access to the software and code used to produce many research results, which has led to a crisis of verifiability and concern about the accuracy of the scientific record? How can digital humanists approach discussions of computational methods, which may not fit into traditional forms of scholarship and can be viewed with suspicion in disciplines that prize the art of scholarly analysis? Computational researchers are examining communication practices, policies, and tools that promise to more effectively convey their research process and the results it produces. The panelists are: Neil Chue Hong, Director of the Software Sustainability Institute; Matthew L. Jockers, Assistant Professor of English at the University of Nebraska-Lincoln; and Daniel P. W. Ellis, Associate Professor of Electrical Engineering at Columbia University.Technical communication, Information sciencede171, vcs2115Statistics, Electrical Engineering, Scholarly Communication Program, Center for Digital Research and Scholarship, Libraries and Information ServicesInterviews and roundtablesMeasuring Scholarly Impact: The Influence of 'Altmetrics'
http://academiccommons.columbia.edu/catalog/ac:165365
Priem, Jason; Holmes, Kristi; Trasande, Caitlin Aptowicz; Gelman, Andrew E.http://hdl.handle.net/10022/AC:P:21698Fri, 20 Sep 2013 00:00:00 +0000"Altmetrics" refers to methods of measuring scholarly impact using Web-based social media. Why does it matter? In many academic fields, attaining scholarly prestige means publishing research articles in important scholarly journals. However, many in the academic community consider a journal's prestige, which is determined by a metric calculated using the number of citations to the journal, to be a poor proxy for the quality of the individual author's work. At the same time, hiring and promotion committees are looking for ways to determine the impact of alternate formats now commonly used by researchers such as blogs, data sets, videos, and social media. The panelists all work with innovative new tools for assessing scholarly impact. They are: Jason Priem, Co-Founder, ImpactStory; Kristi Holmes, Bioinformaticist, Bernard Becker Medical Library, Washington University in St. Louis School of Medicine; and Caitlin Aptowicz Trasande, Head of Science Metrics, Digital Science.Information science, Information technologyag389Statistics, Scholarly Communication Program, Center for Digital Research and Scholarship, Libraries and Information ServicesInterviews and roundtablesGeneralized Volatility-Stabilized Processes
http://academiccommons.columbia.edu/catalog/ac:165162
Pickova, Radkahttp://hdl.handle.net/10022/AC:P:21616Fri, 13 Sep 2013 00:00:00 +0000In this thesis, we consider systems of interacting diffusion processes which we call Generalized Volatility-Stabilized processes, as they extend the Volatility-Stabilized Market models introduced in Fernholz and Karatzas (2005). First, we show how to construct a weak solution of the underlying system of stochastic differential equations. In particular, we express the solution in terms of time-changed squared-Bessel processes and argue that this solution is unique in distribution. In addition, we also discuss sufficient conditions under which this solution does not explode in finite time, and provide sufficient conditions for pathwise uniqueness and for existence of a strong solution. Secondly, we discuss the significance of these processes in the context of Stochastic Portfolio Theory. We describe specific market models which assume that the dynamics of the stocks' capitalizations is the same as that of the Generalized Volatility-Stabilized processes, and we argue that strong relative arbitrage opportunities may exist in these markets, specifically, we provide multiple examples of portfolios that outperform the market portfolio. Moreover, we examine the properties of market weights as well as the diversity weighted portfolio in these models. Thirdly, we provide some asymptotic results for these processes which allows us to describe different properties of the corresponding market models based on these processes.Statisticsrp2424Statistics, MathematicsDissertationsRe-use and Reproducibility: Opportunities and Challenges
http://academiccommons.columbia.edu/catalog/ac:162944
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:20964Tue, 09 Jul 2013 00:00:00 +0000To support the reliability and accuracy of the scientific record, science policy, research infrastructure, and the culture of science must facilitate the sharing of data and code resulting from scientific research, much of which is now produced using computational methods. Though the need to support the reproducibility of computational research is now widely recognized, copyright and other factors present challenges to the development of policies and practices.Technical communication, Information technologyvcs2115StatisticsPresentationsVariability of Universal Life Cash Flows under Higher Risk Investment Strategies
http://academiccommons.columbia.edu/catalog/ac:162700
Tayal, Abhishek; Yang, Canning; Dunn, Thomas P.http://hdl.handle.net/10022/AC:P:20851Thu, 27 Jun 2013 00:00:00 +0000This integrated project studied the offsetting elements of higher nominal yields, greater credit loss expectations, and higher capital requirements on the profitability of the life insurer that pursues a higher yield investment strategy. Profitability measures were developed for a Universal Life product. The report provides an attribution of profit drivers for the insurer. The effects of credit rating migration on credit loss rates and bond capital charges were examined, and investment strategies were tested under credit stress scenarios.Financeat2842, cy2315, tpd2111Statistics, Actuarial SciencesReportsCredit Risk Modeling and Analysis Using Copula Method and Changepoint Approach to Survival Data
http://academiccommons.columbia.edu/catalog/ac:161682
Qian, Bohttp://hdl.handle.net/10022/AC:P:20510Thu, 30 May 2013 00:00:00 +0000This thesis consists of two parts. The first part uses Gaussian Copula and Student's t Copula as the main tools to model the credit risk in securitizations and re-securitizations. The second part proposes a statistical procedure to identify changepoints in Cox model of survival data. The recent 2007-2009 financial crisis has been regarded as the worst financial crisis since the Great Depression by leading economists. The securitization sector took a lot of blame for the crisis because of the connection of the securitized products created from mortgages to the collapse of the housing market. The first part of this thesis explores the relationship between securitized mortgage products and the 2007-2009 financial crisis using the Copula method as the main tool. We show in this part how loss distributions of securitizations and re-securitizations can be derived or calculated in a new model. Simulations are conducted to examine the effectiveness of the model. As an application, the model is also used to examine whether and where the ratings of securitized products could be flawed. On the other hand, the lag effect and saturation effect problems are common and important problems in survival data analysis. They belong to a general class of problems where the treatment effect takes occasional jumps instead of staying constant throughout time. Therefore, they are essentially the changepoint problems in statistics. The second part of this thesis focuses on extending Lai and Xing's recent work in changepoint modeling, which was developed under a time series and Bayesian setup, to the lag effect problems in survival data. A general changepoint approach for Cox model is developed. Simulations and real data analyses are conducted to illustrate the effectiveness of the procedure and how it should be implemented and interpreted.Statisticsbq2102StatisticsDissertationsWhy Public Access to Data is So Important (and why getting the policy right is even more so)
http://academiccommons.columbia.edu/catalog/ac:161424
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:20387Tue, 21 May 2013 00:00:00 +0000Open data is crucial to science today. Computation is becoming central to scientific research. “Open Data” is not well-defined. Scope: Share data and code that permit others in the field to replicate published results. (traditionally done by the publication alone).Information technology, Technical communicationvcs2115StatisticsPresentationsOn optimal arbitrage under constraints
http://academiccommons.columbia.edu/catalog/ac:160495
Sadhukhan, Subhankarhttp://hdl.handle.net/10022/AC:P:20076Wed, 01 May 2013 00:00:00 +0000In this thesis, we investigate the existence of relative arbitrage opportunities in a Markovian model of a financial market, which consists of a bond and stocks, whose prices evolve like Itô processes. We consider markets where investors are constrained to choose from among a restricted set of investment strategies. We show that the upper hedging price of (i.e. the minimum amount of wealth needed to superreplicate) a given contingent claim in a constrained market can be expressed as the supremum of the fair price of the given contingent claim under certain unconstrained auxiliary Markovian markets. Under suitable assumptions, we further characterize the upper hedging price as viscosity solution to certain variational inequalities. We, then, use this viscosity solution characterization to study how the imposition of stricter constraints on the market affect the upper hedging price. In particular, if relative arbitrage opportunities exist with respect to a given strategy, we study how stricter constraints can make such arbitrage opportunities disappear.Applied mathematics, Financess3240Statistics, MathematicsDissertationsStatistical Inference for Diagnostic Classification Models
http://academiccommons.columbia.edu/catalog/ac:160464
Xu, Gongjunhttp://hdl.handle.net/10022/AC:P:20058Tue, 30 Apr 2013 00:00:00 +0000Diagnostic classification models (DCM) are an important recent development in educational and psychological testing. Instead of an overall test score, a diagnostic test provides each subject with a profile detailing the concepts and skills (often called "attributes") that he/she has mastered. Central to many DCMs is the so-called Q-matrix, an incidence matrix specifying the item-attribute relationship. It is common practice for the Q-matrix to be specified by experts when items are written, rather than through data-driven calibration. Such a non-empirical approach may lead to misspecification of the Q-matrix and substantial lack of model fit, resulting in erroneous interpretation of testing results. This motivates our study and we consider the identifiability, estimation, and hypothesis testing of the Q-matrix. In addition, we study the identifiability of diagnostic model parameters under a known Q-matrix. The first part of this thesis is concerned with estimation of the Q-matrix. In particular, we present definitive answers to the learnability of the Q-matrix for one of the most commonly used models, the DINA model, by specifying a set of sufficient conditions under which the Q-matrix is identifiable up to an explicitly defined equivalence class. We also present the corresponding data-driven construction of the Q-matrix. The results and analysis strategies are general in the sense that they can be further extended to other diagnostic models. The second part of the thesis focuses on statistical validation of the Q-matrix. The purpose of this study is to provide a statistical procedure to help decide whether to accept the Q-matrix provided by the experts. Statistically, this problem can be formulated as a pure significance testing problem with null hypothesis H0 : Q = Q0, where Q0 is the candidate Q-matrix. We propose a test statistic that measures the consistency of observed data with the proposed Q-matrix. Theoretical properties of the test statistic are studied. In addition, we conduct simulation studies to show the performance of the proposed procedure. The third part of this thesis is concerned with the identifiability of the diagnostic model parameters when the Q-matrix is correctly specified. Identifiability is a prerequisite for statistical inference, such as parameter estimation and hypothesis testing. We present sufficient and necessary conditions under which the model parameters are identifiable from the response data.Statistics, Educational tests and measurementsgx2108StatisticsDissertationsTestimony submitted to the House Committee on Science, Space and Technology for the March 5, 2013 hearing on Scientific Integrity and Transparency.
http://academiccommons.columbia.edu/catalog/ac:157889
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:19394Thu, 21 Mar 2013 00:00:00 +0000Reproducibility is a new challenge, brought about by advances in scientific research capability due to immense changes in technology over the last two decades. It is widely recognized as a defining hallmark of science and directly impacts the transparency and reliability of findings, and is taken very seriously by the scientific community.Technical communication, Information technologyvcs2115StatisticsPresentationsTechnology and the Scientific Method: The Credibility Crisis in Computational Science
http://academiccommons.columbia.edu/catalog/ac:157876
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:19391Thu, 21 Mar 2013 00:00:00 +0000Computation presents only a potential third branch of the scientific method.Technical communication, Information technologyvcs2115StatisticsPresentationsDigital Scholarship in Scientific Research: Open Questions in Reproducibility and Curation.
http://academiccommons.columbia.edu/catalog/ac:157879
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:19392Thu, 21 Mar 2013 00:00:00 +0000Computation presents only a potential third branch of the scientific method.Technical communication, Information technologyvcs2115StatisticsPresentationsOpen Data, Open Methods, and the Promise of Large Scale Validation.
http://academiccommons.columbia.edu/catalog/ac:157883
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:19393Thu, 21 Mar 2013 00:00:00 +0000Reproducibility is core to science, and a critical issue in computational science,Technical communication, Information technologyvcs2115StatisticsPresentationsFacilitating Reproducibility: Open Data and Code in Economics
http://academiccommons.columbia.edu/catalog/ac:157873
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:19390Thu, 21 Mar 2013 00:00:00 +0000The aim of the workshop is to build an understanding of the value of open data and open tools for the Economics profession and the obstacles to opening up information, as well as the role of greater openness in broadening understanding of and engagement with Economics among the wider community including policy-makers and society.Technical communication, Economicsvcs2115StatisticsPresentationsBayesian Model Selection in terms of Kullback-Leibler discrepancy
http://academiccommons.columbia.edu/catalog/ac:158374
Zhou, Shouhaohttp://hdl.handle.net/10022/AC:P:19157Mon, 25 Feb 2013 00:00:00 +0000In this article we investigate and develop the practical model assessment and selection methods for Bayesian models, when we anticipate that a promising approach should be objective enough to accept, easy enough to understand, general enough to apply, simple enough to compute and coherent enough to interpret. We mainly restrict attention to the Kullback-Leibler divergence, a widely applied model evaluation measurement to quantify the similarity between the proposed candidate model and the underlying true model, where the true model is only referred to a probability distribution as the best projection onto the statistical modeling space once we try to understand the real but unknown dynamics/mechanism of interest. In addition to review and discussion on the advantages and disadvantages of the historically and currently prevailing practical model selection methods in literature, a series of convenient and useful tools, each designed and applied for different purposes, are proposed to asymptotically unbiasedly assess how the candidate Bayesian models are favored in terms of predicting a future independent observation. What's more, we also explore the connection of the Kullback-Leibler based information criterion to the Bayes factors, another most popular Bayesian model comparison approaches, after seeing the motivation through the developments of the Bayes factor variants. In general, we expect to provide a useful guidance for researchers who are interested in conducting Bayesian data analysis.Statisticssz2020StatisticsDissertationsMultiplicative Multiresolution Analysis for Lie-group Valued Data Indexed by a Euclidean Parameter
http://academiccommons.columbia.edu/catalog/ac:155756
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15397Wed, 12 Dec 2012 00:00:00 +0000Lie-valued euclidean indexed data. These data might be: phase angles as functions of time or space, for example compass directions; 3D orientations of a rigid frame of reference as a function of time or space; or, quaternions as a function of time or space. This can also be extended to quotients of lie groups which gives us the ability to model points on S2, the unit sphere, as functions of time or space.Computer science, Statisticsvcs2115StatisticsPresentationsA Brief History of the Reproducibility Movement
http://academiccommons.columbia.edu/catalog/ac:155759
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15396Wed, 12 Dec 2012 00:00:00 +0000Computational science cannot be elevated to a third branch of the scientific method until it generates routinely verifiable knowledge.Technical communication, Computer sciencevcs2115StatisticsPresentationsTransparency in Computational Science
http://academiccommons.columbia.edu/catalog/ac:154852
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15360Tue, 27 Nov 2012 00:00:00 +0000The central motivation for the scientific method is to root out error: Computational science as practiced today does not generate reliable knowledge. This presentation looks at four possible solutions to the issues of transparency in computational science.Technical communication, Computer sciencevcs2115StatisticsPresentationsRunMyCode.org: a Novel Dissemination and Collaboration Platform for Executing Published Computational Results
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15349Wed, 21 Nov 2012 00:00:00 +0000A presentation on a collaboration platform for executing published computational results.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsJournal Policy and Reproducible Computational Research
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15348Wed, 21 Nov 2012 00:00:00 +0000Discusses policy possibilities for the issues of reproducibility and dissemination in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsTowards Reproducible Science: Policy and a Path Forward
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15347Wed, 21 Nov 2012 00:00:00 +0000Discusses solutions and policy possibilities for the issues of reproducibility and dissemination in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsDiscussant: “Pornography and Divorce”
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15350Wed, 21 Nov 2012 00:00:00 +0000A presentation on data and design suggestions for research on the topic of pornography and divorce.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsSegregation in Social Networks Based on Acquaintanceship and Trust
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DiPrete, Thomas A.; Gelman, Andrew E.; McCormick, Tyler; Teitler, Julien O.; Zheng, Tianhttp://hdl.handle.net/10022/AC:P:15339Tue, 20 Nov 2012 00:00:00 +0000Using 2006 General Social Survey data, the authors compare levels of segregation by race and along other dimensions of potential social cleavage in the contemporary United States. Americans are not as isolated as the most extreme recent estimates suggest. However, hopes that “bridging” social capital is more common in broader acquaintanceship networks than in core networks are not supported. Instead, the entire acquaintanceship network is perceived by Americans to be about as segregated as the much smaller network of close ties. People do not always know the religiosity, political ideology, family behaviors, or socioeconomic status of their acquaintances, but perceived social divisions on these dimensions are high, sometimes rivaling racial segregation in acquaintanceship networks. The major challenge to social integration today comes from the tendency of many Americans to isolate themselves from others who differ on race, political ideology, level of religiosity, and other salient aspects of social identity.Statisticstad61, ag389 , thm2105, jot8, tz33Political Science, Sociology, Statistics, Social WorkArticlesMultiple Imputation with Diagnostics (mi) in R: Opening Windows into the Black Box
http://academiccommons.columbia.edu/catalog/ac:154731
Su, Yu-Sung; Yajima, Masanao; Gelman, Andrew E.; Hill, Jenniferhttp://hdl.handle.net/10022/AC:P:15342Tue, 20 Nov 2012 00:00:00 +0000Our mi package in R has several features that allow the user to get inside the imputation process and evaluate the reasonableness of the resulting models and imputations. These features include: choice of predictors, models, and transformations for chained imputation models; standard and binned residual plots for checking the fit of the conditional distributions used for imputation; and plots for comparing the distributions of observed and imputed data. In addition, we use Bayesian models and weakly informative prior distributions to construct more stable estimates of imputation models. Our goal is to have a demonstration package that (a) avoids many of the practical problems that arise with existing multivariate imputation programs, and (b) demonstrates state-of-the-art diagnostics that can be applied more generally and can be incorporated into the software of others.Statisticsag389 Political Science, StatisticsArticlesR2WinBUGS: A Package for Running WinBUGS from R
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Sturtz, Sibylle; Ligges, Uwe; Gelman, Andrew E.http://hdl.handle.net/10022/AC:P:15341Tue, 20 Nov 2012 00:00:00 +0000The R2WinBUGS package provides convenient functions to call WinBUGS from R. It automatically writes the data and scripts in a format readable by WinBUGS for processing in batch mode, which is possible since version 1.4. After the WinBUGS process has finished, it is possible either to read the resulting data into R by the package itself—which gives a compact graphical summary of inference and convergence diagnostics—or to use the facilities of the coda package for further analyses of the output. Examples are given to demonstrate the usage of this package.Statisticsag389 Political Science, StatisticsArticlesBayesian Statistical Pragmatism
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Gelman, Andrew E.http://hdl.handle.net/10022/AC:P:15340Tue, 20 Nov 2012 00:00:00 +0000I agree with Rob Kass’ point that we can and should make use of statistical methods developed under different philosophies, and I am happy to take the opportunity to elaborate on some of his arguments.Statisticsag389 Political Science, StatisticsArticlesThe Reproducible Research Movement: Crisis and Solutions
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15326Tue, 20 Nov 2012 00:00:00 +0000Discusses solutions to the reproducibility of computational research in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsDisseminating Numerically Reproducible Research
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15325Tue, 20 Nov 2012 00:00:00 +0000Discusses solutions to the reproducible computational research in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsSoftware Patents as a Barrier to Scientific Transparency: An Unexpected Consequence of Bayh-Dole
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Reich, Isabel Rose ; Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15328Tue, 20 Nov 2012 00:00:00 +0000Discusses solutions to the reproducibility and dissemination issues in computational science. Examines the interaction between the digitization of science and Intellectual Property Law, specifically the incentives created by the Bayh‐Dole Act to patent inventions associated with university‐based research.Technical communication, Intellectual propertyirr2105, vcs2115Applied Physics and Applied Mathematics, StatisticsPresentationsData-Intensive Science: Methods for Reproducibility and Dissemination
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:15327Tue, 20 Nov 2012 00:00:00 +0000Discusses solutions to the reproducibility dissemination issues in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsContributions to Semiparametric Inference to Biased-Sampled and Financial Data
http://academiccommons.columbia.edu/catalog/ac:177018
Sit, Tonyhttp://hdl.handle.net/10022/AC:P:14685Wed, 12 Sep 2012 00:00:00 +0000This thesis develops statistical models and methods for the analysis of life-time and financial data under the umbrella of semiparametric framework. The first part studies the use of empirical likelihood on Levy processes that are used to model the dynamics exhibited in the financial data. The second part is a study of inferential procedure for survival data collected under various biased sampling schemes in transformation and the accelerated failure time models. During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derivative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood methods to estimate the parameters of various diffusion processes via their characteristic functions which are readily available in most cases. Return series from the market are used for estimation. In addition to the return series, there are many derivatives actively traded in the market whose prices also contain information about parameters of the underlying process. This observation motivates us to combine the return series and the associated derivative prices observed at the market so as to provide a more reflective estimation with respect to the market movement and achieve a gain in efficiency. The usual asymptotic properties, including consistency and asymptotic normality, are established under suitable regularity conditions. We performed simulation and case studies to demonstrate the feasibility and effectiveness of the proposed method. The second part of this thesis investigates a unified estimation method for semiparametric linear transformation models and accelerated failure time model under general biased sampling schemes. The methodology proposed is first investigated in Paik (2009) in which the length-biased case is considered for transformation models. The new estimator is obtained from a set of counting process-based unbiased estimating equations, developed through introducing a general weighting scheme that offsets the sampling bias. The usual asymptotic properties, including consistency and asymptotic normality, are established under suitable regularity conditions. A closed-form formula is derived for the limiting variance and the plug-in estimator is shown to be consistent. We demonstrate the unified approach through the special cases of left truncation, length-bias, the case-cohort design and variants thereof. Simulation studies and applications to real data sets are also presented.Statisticsts2500StatisticsDissertationsMethods for studying the neural code in high dimensions
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Ramirez, Alexandro D.http://hdl.handle.net/10022/AC:P:14688Wed, 12 Sep 2012 00:00:00 +0000Over the last two decades technological developments in multi-electrode arrays and fluorescence microscopy have made it possible to simultaneously record from hundreds to thousands of neurons. Developing methods for analyzing these data in order to learn how networks of neurons respond to external stimuli and process information is an outstanding challenge for neuroscience. In this dissertation, I address the challenge of developing and testing models that are both flexible and computationally tractable when used with high dimensional data. In chapter 2 I will discuss an approximation to the generalized linear model (GLM) log-likelihood that I developed in collaboration with my thesis advisor. This approximation is designed to ease the computational burden of evaluating GLMs. I will show that our method reduces the computational cost of evaluating the GLM log-likelihood by a factor proportional to the number of parameters in the model times the number of observations. Therefore it is most beneficial in typical neuroscience applications where the number of parameters is large. I then detail a variety of applications where our method can be of use, including Maximum Likelihood estimation of GLM parameters, marginal likelihood calculations for model selection and Markov chain Monte Carlo methods for sampling from posterior parameter distributions. I go on to show that our model does not necessarily sacrifice accuracy for speed. Using both analytic calculations and multi-unit, primate retinal responses, I show that parameter estimates and predictions using our model can have the same accuracy as that of generalized linear models. In chapter 3 I study the neural decoding problem of predicting stimuli from neuronal responses. The focus is on reconstructing zebra finch song spectrograms, which are high-dimensional, by combining the spike trains of zebra finch auditory midbrain neurons with information about the correlations present in all zebra finch song. I use a GLM to model neuronal responses and a series of prior distributions, each carrying different amounts of statistical information about zebra finch song. For song reconstruction I make use of recent connections made between the applied mathematics literature on solving linear systems of equations involving matrices with special structure and neural decoding. This allowed me to calculate \textit{maximum a posteriori} (MAP) estimates of song spectrograms in a time that only grows linearly, and is therefore quite tractable, with the number of time-bins in the song spectrogram. This speed was beneficial for answering questions which required the reconstruction of a variety of song spectrograms each corresponding to different priors made on the distribution of zebra finch song. My collaborators and I found that spike trains from a population of MLd neurons combined with an uncorrelated Gaussian prior can estimate the amplitude envelope of song spectrograms. The same set of responses can be combined with Gaussian priors that have correlations matched to those found across multiple zebra finch songs to yield song spectrograms similar to those presented to the animal. The fidelity of spectrogram reconstructions from MLd responses relies more heavily on prior knowledge of spectral correlations than temporal correlations. However the best reconstructions combine MLd responses with both spectral and temporal correlations.Neurosciencesadr2110Statistics, Neurobiology and Behavior, NeuroscienceDissertationsDetecting Dependence Change Points in Multivariate Time Series with Applications in Neuroscience and Finance
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Cribben, Ivor Johnhttp://hdl.handle.net/10022/AC:P:14681Wed, 12 Sep 2012 00:00:00 +0000In many applications there are dynamic changes in the dependency structure between multivariate time series. Two examples include neuroscience and finance. The second and third chapters focus on neuroscience and introduce a data-driven technique for partitioning a time course into distinct temporal intervals with different multivariate functional connectivity patterns between a set of brain regions of interest (ROIs). The technique, called Dynamic Connectivity Regression (DCR), detects temporal change points in functional connectivity and estimates a graph, or set of relationships between ROIs, for data in the temporal partition that falls between pairs of change points. Hence, DCR allows for estimation of both the time of change in connectivity and the connectivity graph for each partition, without requiring prior knowledge of the nature of the experimental design. Permutation and bootstrapping methods are used to perform inference on the change points. In the second chapter of this work, we focus on multi-subject data while in the third chapter, we concentrate on single-subject data and extend the DCR methodology in two ways: (i) we alter the algorithm to make it more accurate for individual subject data with a small number of observations and (ii) we perform inference on the edges or connections between brain regions in order to reduce the number of false positives in the graphs. We also discuss a Likelihood Ratio test to compare precision matrices (inverse covariance matrices) across subjects as well as a test across subjects on the single edges or partial correlations in the graph. In the final chapter of this work, we turn to a finance setting. We use the same DCR technique to detect changes in dependency structure in multivariate financial time series for situations where both the placement and number of change points is unknown. In this setting, DCR finds the dependence change points and estimates an undirected graph representing the relationship between time series within each interval created by pairs of adjacent change points. A shortcoming of the proposed DCR methodology is the presence of an excessive number of false positive edges in the undirected graphs, especially when the data deviates from normality. Here we address this shortcoming by proposing a procedure for performing inference on the edges, or partial dependencies between time series, that effectively removes false positive edges. We also discuss two robust estimation procedures based on ranks and the tlasso (Finegold and Drton, 2011) technique, which we contrast with the glasso technique used by DCR.Statisticsijc2104StatisticsDissertationsModeling Strategies for Large Dimensional Vector Autoregressions
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Zang, Pengfeihttp://hdl.handle.net/10022/AC:P:14666Tue, 11 Sep 2012 00:00:00 +0000The vector autoregressive (VAR) model has been widely used for describing the dynamic behavior of multivariate time series. However, fitting standard VAR models to large dimensional time series is challenging primarily due to the large number of parameters involved. In this thesis, we propose two strategies for fitting large dimensional VAR models. The first strategy involves reducing the number of non-zero entries in the autoregressive (AR) coefficient matrices and the second is a method to reduce the effective dimension of the white noise covariance matrix. We propose a 2-stage approach for fitting large dimensional VAR models where many of the AR coefficients are zero. The first stage provides initial selection of non-zero AR coefficients by taking advantage of the properties of partial spectral coherence (PSC) in conjunction with BIC. The second stage, based on $t$-ratios and BIC, further refines the spurious non-zero AR coefficients post first stage. Our simulation study suggests that the 2-stage approach outperforms Lasso-type methods in discovering sparsity patterns in AR coefficient matrices of VAR models. The performance of our 2-stage approach is also illustrated with three real data examples. Our second strategy for reducing the complexity of a large dimensional VAR model is based on a reduced-rank estimator for the white noise covariance matrix. We first derive the reduced-rank covariance estimator under the setting of independent observations and give the analytical form of its maximum likelihood estimate. Then we describe how to integrate the proposed reduced-rank estimator into the fitting of large dimensional VAR models, where we consider two scenarios that require different model fitting procedures. In the VAR modeling context, our reduced-rank covariance estimator not only provides interpretable descriptions of the dependence structure of VAR processes but also leads to improvement in model-fitting and forecasting over unrestricted covariance estimators. Two real data examples are presented to illustrate these fitting procedures.Statisticspz2146StatisticsDissertationsSome Models for Time Series of Counts
http://academiccommons.columbia.edu/catalog/ac:152149
Liu, Henghttp://hdl.handle.net/10022/AC:P:14561Wed, 29 Aug 2012 00:00:00 +0000This thesis focuses on developing nonlinear time series models and establishing relevant theory with a view towards applications in which the responses are integer valued. The discreteness of the observations, which is not appropriate with classical time series models, requires novel modeling strategies. The majority of the existing models for time series of counts assume that the observations follow a Poisson distribution conditional on an accompanying intensity process that drives the serial dynamics of the model. According to whether the evolution of the intensity process depends on the observations or solely on an external process, the models are classified into parameter-driven and observation-driven. Compared to the former one, an observation-driven model often allows for easier and more straightforward estimation of the model parameters. On the other hand, the stability properties of the process, such as the existence and uniqueness of a stationary and ergodic solution that are required for deriving asymptotic theory of the parameter estimates, can be quite complicated to establish, as compared to parameter-driven models. In this thesis, we first propose a broad class of observation-driven models that is based upon a one-parameter exponential family of distributions and incorporates nonlinear dynamics. The establishment of stability properties of these processes, which is at the heart of this thesis, is addressed by employing theory from iterated random functions and coupling techniques. Using this theory, we are also able to obtain the asymptotic behavior of maximum likelihood estimates of the parameters. Extensions of the base model in several directions are considered. Inspired by the idea of a self-excited threshold ARMA process, a threshold Poisson autoregression is proposed. It introduces a two-regime structure in the intensity process and essentially allows for modeling negatively correlated observations. E-chain, a non-standard Markov chain technique and Lyapunov's method are utilized to show the stationarity and a law of large numbers for this process. In addition, the model has been adapted to incorporate covariates, an important problem of practical and primary interest. The base model is also extended to consider the case of multivariate time series of counts. Given a suitable definition of a multivariate Poisson distribution, a multivariate Poisson autoregression process is described and its properties studied. Several simulation studies are presented to illustrate the inference theory. The proposed models are also applied to several real data sets, including the number of transactions of the Ericsson stock, the return times of Goldman Sachs Group stock prices, the number of road crashes in Schiphol, the frequencies of occurrences of gold particles, the incidences of polio in the US and the number of presentations of asthma in an Australian hospital. An array of graphical and quantitative diagnostic tools, which is specifically designed for the evaluation of goodness of fit for time series of counts models, is described and illustrated with these data sets.Statisticshl2494StatisticsDissertationsStatistical inference in two non-standard regression problems
http://academiccommons.columbia.edu/catalog/ac:151460
Seijo, Emilio Franciscohttp://hdl.handle.net/10022/AC:P:14317Wed, 08 Aug 2012 00:00:00 +0000This thesis analyzes two regression models in which their respective least squares estimators have nonstandard asymptotics. It is divided in an introduction and two parts. The introduction motivates the study of nonstandard problems and presents an outline of the contents of the remaining chapters. In part I, the least squares estimator of a multivariate convex regression function is studied in great detail. The main contribution here is a proof of the consistency of the aforementioned estimator in a completely nonparametric setting. Model misspecification, local rates of convergence and multidimensional regression models mixing convexity and componentwise monotonicity constraints will also be considered. Part II deals with change-point regression models and the issues that might arise when applying the bootstrap to these problems. The classical bootstrap is shown to be inconsistent on a simple change-point regression model, and an alternative (smoothed) bootstrap procedure is proposed and proved to be consistent. The superiority of the alternative method is also illustrated through a simulation study. In addition, a version of the continuous mapping theorem specially suited for change-point estimators is proved and used to derive the results concerning the bootstrap.Statistics, Applied mathematics, Mathematicsefs2113StatisticsDissertationsCopyright and MetaData in the World Heritage Digital Mathematical Library
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:13485Mon, 11 Jun 2012 00:00:00 +0000A power-point presentation covering 4 points covering Copyright and MetaData in the World Heritage Digital Mathematical Library.Intellectual property, Library sciencevcs2115StatisticsPresentationsThe Reproducible Computational Science Movement: Tools, Policy, and Results
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:13488Mon, 11 Jun 2012 00:00:00 +0000Discusses solutions to the credibility crisis in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsTransparency in Scientific Discovery: Innovation and Knowledge Dissemination
http://academiccommons.columbia.edu/catalog/ac:147781
Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:13496Mon, 11 Jun 2012 00:00:00 +0000Discusses solutions to the credibility crisis in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentationsThe Credibility Crisis in Computational Science: An Information Issue
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Stodden, Victoria C.http://hdl.handle.net/10022/AC:P:13489Mon, 11 Jun 2012 00:00:00 +0000Discusses solutions to the credibility crisis in computational science.Technical communication, Intellectual propertyvcs2115StatisticsPresentations