Bayesian Model Selection
Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. the quality of these solutions usually depends on the quality of the constructed Bayesian models.
A default framework for the Bayesian model selection is based on the Bayes factor.
From the Bayes factor, Bayesian information criterion (BIC), generalized Bayesian information criterion (GBIC), and various types of Bayesian model selection criteria have been proposed.
Sampling Methods
The Bayesian inference on a statistical model was previously complex. It is now possible to implement the various types of the Bayesian inference thanks to advances in computing technology and the use of new sampling methods, including Markov chain Monte Carlo (MCMC).
Bayesian Modeling Averaging
By averaging over many different Bayesian statistical models, it can incorporate model uncertainty into the solution of the decision problems.
Reference
Bayesian Model Selection and Statistical Modeling by Tomohiro Ando