Bayesian Approaches for Comparing Nonnested Models

Abstract

Model comparison and model assessment are a crucial part of statistical analysis. Due to recent computational advances, sophisticated techniques for Bayesian model assessment are becoming increasingly popular. We have seen a recent surge in the statistical literature on Bayesian methods for model assessment and model comparison, including articles by George and McCulloch (1993), Madigan and Raftery (1994), Ibrahim and Laud (1994), Laud and Ibrahim (1995), Kass and Raftery (1995), Chib (1995), Chib and Greenberg (1998), Raftery, Madigan, and Volinsky (1995), George, McCulloch, and Tsay (1996), Raftery, Madigan, and Hooting (1997), Gelfand and Ghosh (1998), Clyde (1999), Sinha, Chen, and Ghosh (1999), Ibrahim, Chen, and Sinha (1998), Ibrahim and Chen (1998), Ibrahim, Chen, and MacEachern (1999), and Chen, Ibrahim, and Yiannoutsos (1999). The scope of Bayesian model comparison and model assessment is quite broad, and can be investigated via Bayes factors, model diagnostics, and goodness of fit measures. In many situations, one may want to compare several models which are not nested. In this particular context, we consider model comparison using marginal likelihood approaches, “super-model” or “sub-model” approaches, and criterion-based methods. The computational techniques involved in these three approaches will be addressed in detail. In addition, several important applications, including scale mixtures of multi-variate normal link models and Bayesian discretized scmiparametric models for interval-censored data, will be presented.