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Activity Number: 139
Type: Contributed
Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #318775
Title: Nonlocal Functional Priors for Nonparametric Bayesian Testing
Author(s): Minsuk Shin* and Valen E. Johnson and Anirban Bhattacharya
Companies: Texas A&M University and Texas A&M University and Texas A&M University
Keywords: Bayes factor ; Goodness-of-fit test ; Nonlocal prior ; Nonparametric regression ; Vayring coefficient model

We show that the prior densities, which assign positive probability around null function in nonparametric Bayesian test, provide exponential accumulation of evidence in favor of alternative hypothesis under a true alternative, but only a polynomical rate of accumulation in favor of null hypothesis under true null. This imbalanced behavior of Bayes factor thus prevents the resulting tests from obtaining strong evidence in favor of a null hypothesis even when a moderate size of samples is available. We propose two new classes of alternative prior densities that ameliorate the asymmetry in the asymptotic rate of Bayes factor. Using the proposed priors, we provide some examples that are applied to hypothesis tests for the nonparametric regression model and the varying coefficient model.

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

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