2017/05/16_Jeffrey Hart, Texas A&M University, USA

Prior-free Bayes Factors Based on Data Splitting

2017/05/16 – 12:00 h | Jeffrey Hart, Texas A&M University, USA

Abstract

A method of computing Bayes factors for comparison of two models is proposed. The method has a number of advantages, including relative computational simplicity, no need for prior distributions and Bayes consistency at an exponential rate under both models. The idea uses data splitting. Maximum likelihood estimates of the two models are obtained from a subset of data, and then a likelihood ratio comparing the estimated models is computed from the remainder of the data. This likelihood ratio is a legitimate Bayes factor since the two models being compared come from outside the data used to compute the likelihood ratio. The asymptotic behavior (as sample size tends to infinity) of the Bayes factor will be described, and a simulation study will explore the practical question of how large the two subsets of data should be. Finally, we provide an example involving a regression analysis of concrete compressive strength.