Back to Search Start Over

A novel approach to Bayesian consistency

Authors :
Minwoo Chae
Stephen G. Walker
Source :
Electron. J. Statist. 11, no. 2 (2017), 4723-4745
Publication Year :
2017
Publisher :
Institute of Mathematical Statistics, 2017.

Abstract

It is well-known that the Kullback–Leibler support condition implies posterior consistency in the weak topology, but is not sufficient for consistency in the total variation distance. There is a counter–example. Since then many authors have proposed sufficient conditions for strong consistency; and the aim of the present paper is to introduce new conditions with specific application to nonparametric mixture models with heavy–tailed components, such as the Student-$t$. The key is a more focused result on sets of densities where if strong consistency fails then it fails on such densities. This allows us to move away from the traditional types of sieves currently employed.

Details

ISSN :
19357524
Volume :
11
Database :
OpenAIRE
Journal :
Electronic Journal of Statistics
Accession number :
edsair.doi.dedup.....77fbcda587dca03dd86e33420bb75546