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Activity Number: 397 - Multiple Aspects of Bayesian Strategies for Variable Selection in Standard and Non-Standard Models
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #301708 Presentation
Title: Bayesian Model Selection for Nonparametric Problems
Author(s): Debdeep Pati* and Yun Yang
Companies: Texas A&M University and University of Illinois Urbana-Champaign

In this talk, we investigate large sample properties of model selection procedures in a nonparametric Bayesian framework when a closed form expression of the marginal likelihood function is not available or a local asymptotic quadratic approximation of the log-likelihood function does not exist. Under appropriate identifiability assumptions on the true model, we provide sufficient conditions for a Bayesian model selection procedure to be consistent and obey the Occam's razor phenomenon, i.e., the probability of selecting the ``smallest" model that contains the truth tends to one as the sample size goes to infinity. In order to show that a Bayesian model selection procedure selects the smallest model containing the truth, we impose a prior anti-concentration condition, requiring the prior mass assigned by large models to a neighborhood of the truth to be sufficiently small. In a more general setting where the strong model separation gap assumption may not hold, we introduce the notion of local Bayesian complexity and develop oracle inequalities for Bayesian model selection procedures.

Authors who are presenting talks have a * after their name.

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