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A Direct Approach to Understanding Posterior Consistency of Bayesian Regression Problems

Authors
Yi, SeongbaekChoi, Taeryon
Issue Date
2011
Publisher
TAYLOR & FRANCIS INC
Keywords
Nonparametric regression; Orthogonality; Posterior density consistency; Quadratic form; Sample size dependent prior
Citation
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, v.40, no.18, pp.3315 - 3326
Indexed
SCIE
SCOPUS
Journal Title
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume
40
Number
18
Start Page
3315
End Page
3326
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/114931
DOI
10.1080/03610926.2010.498646
ISSN
0361-0926
Abstract
Previous approaches to establishing posterior consistency of Bayesian regression problems have used general theorems that involve verifying sufficient conditions for posterior consistency. In this article, we consider a direct approach by computing the posterior density explicitly and evaluating its asymptotic behavior. For this purpose, we deal with a sample size dependent prior based on a truncated regression function with increasing sample size, and evaluate the asymptotic properties of the resulting posterior. Based on a concept called posterior density consistency, we attempt to understand posterior consistency. As an application, we illustrate that the posterior density of an orthogonal semiparametric regression model is consistent.
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