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Non-Bayesian Inference and Prediction

Di Xiao

Title:
Non-Bayesian Inference and Prediction
Author(s):
Xiao, Di
Thesis Advisor(s):
He, Xuedong
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Industrial Engineering and Operations Research
Persistent URL:
Abstract:
In this thesis, we first propose a coherent inference model that is obtained by distorting the prior density in Bayes' rule and replacing the likelihood with a so-called pseudo-likelihood. This model includes the existing non-Bayesian inference models as special cases and implies new models of base-rate neglect and conservatism. We prove a sufficient and necessary condition under which the coherent inference model is processing consistent, i.e., implies the same posterior density however the samples are grouped and processed retrospectively. We show that processing consistency does not imply Bayes' rule by proving a sufficient and necessary condition under which the coherent inference model can be obtained by applying Bayes' rule to a false stochastic model. We then propose a prediction model that combines a stochastic model with certain parameters and a processing-consistent, coherent inference model. We show that this prediction model is processing consistent, which states that the prediction of samples does not depend on how they are grouped and processed prospectively, if and only if this model is Bayesian. Finally, we apply the new model of conservatism to a car selection problem, a consumption-based asset pricing model, and a regime-switching asset pricing model.
Subject(s):
Operations research
Mathematical statistics
Industrial engineering
Item views
28
Metadata:
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Suggested Citation:
Di Xiao, , Non-Bayesian Inference and Prediction, Columbia University Academic Commons, .

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