FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 13-34

Bayesian model selection and the concentration of the posterior of hyperparameters

N. P. Baldin
V. G. Spokoiny

Abstract

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The present paper offers a construction of a hyperprior that can be used for Bayesian model selection. This construction is inspired by the idea of the unbiased model selection in a penalized maximum likelihood approach. The main result shows a one-sided contraction of the posterior: the posterior mass is allocated on models of lower complexity than the oracle one.

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Last modified: January 7, 2014