Bayesian Model Selection and Hypothesis Tests

Model comparison remains an active research frontier in Bayesian analysis. The chapter introduces related specific research problems, including the selection of a number of components in a mixture model and the choice of a training sample size when using virtual simulated training samples. The chapter also discusses an intriguing general property that sets Bayesian testing apart from frequentist testing, by effectively rewarding honest choice of an alternative hypothesis. Cheating does not pay.