Highlights from Bayesian Analysis

• Activity Number: 319 - Highlights from Bayesian Analysis
• Type: Invited
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Christopher C Drovandi* and Kerrie Mengersen and Michael Evans and David J Nott
• Companies: Queensland University of Technology and Queensland University of Technology and University of Toronto and National University of Singapore
• Keywords: ABC; Bayesian Inference; Bayesian p-values; posterior predictive check; prior predictive check; weakly informative prior

Abstract

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. The second problem considered is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful.