Bayesian cross-validation choice and assessment of statistical models

This thesis will be concerned with application of a cross-validation criterion to the choice and assessment of statistical models, in which observed data are partitioned, with one part of the data compared to predictions conditional on the model and the rest of the data. We develop three methods, gold, silver, and bronze based on the idea of splitting data in the context of measuring prediction error; however, they can also be adapted for model checking. The gold method uses analytic calculations for the posterior predictive distribution; however, the silver method avoids this mathematical intensity, instead simulating many posterior samples, and the bronze method reduces the amount of sampling to speed up computation. We also consider the Bayesian p-value in which the posterior distribution can be used to check model adequacy, in the context of cross-validation with repeated data splitting. Application to examples is detailed, using the discussed methodologies of estimation and prediction.Science, Faculty ofStatistics, Department ofGraduat