Adaptive MCMC Using Stratified Proposals for Bayesian and Frequentist Inference

• Activity Number: 228
• Type: Invited
• Date/Time: Tuesday, July 31, 2007 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Mylène Bédard*+ and Donald A.S. Fraser and Augustive C.M. Wong
• Companies: University of Warwick and University of Toronto and York University
• Keywords: Metropolis-Hastings algorithm ; Adaptive MCMC method ; Frequentist vs. Bayesian ; Regression example

Abstract

In this talk, we study the equivalence between frequentist p-values and their corresponding Bayesian posterior survivor values (s-values), obtained when choosing a not too subjective prior. This is achieved by considering a simple regression example for which exact calculations can be obtained, and testing various hypotheses for the regression parameters. We then validate the obtained p-values and s-values using MCMC methods, which verify that they are uniformly distributed over (0,1) conditionally on some information provided by the data. We assess the numerical values for accuracy using the traditional Metropolis-Hastings algorithm, and we also use the asymptotic properties of our regression example to propose two different adaptive algorithms. These lead to a significant increase of the acceptance rate, meaning that the methods propose moves in a more wisely determined manner.