Spatial Bayesian Model Selection with Nonlocal Prior Open Access

Ding, Tianyu (2015)

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A common objective of Bayesian spatial variable selection for regression models is to select important spatially distributed predictors that are strongly associated with the outcome. Many Bayesian variable selection procedures use local priors which do not have posterior variable selection consistency. We propose a novel spatial Bayesian model selection procedure based on nonlocal prior with incorporating spatial depen- dence of predictors. It show been shown that the Bayesian model selection procedure with nonlocal prior enjoys good theoretical properties and achieves better perfor- mance than existing methods. In this thesis, we show that incorporating the spatial dependence between the predictors can improve the nonlocal prior based Bayesian variable selection procedure in terms of both selection accuracy and prediction accu- racy. We demonstrate the advantages of our method via simulation studies and an analysis of the brain imaging data from an Autism study.

Table of Contents

1 Introduction

2 The Model

2.1 Nonlocal Priors with Spatial Dependence

2.2 Normalizing Constant Computation

3 Simulation Studies

4 Real Data Studies

5 Discussion Appendices

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  • English
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