Essays on cross-validation methods for Bayesian models of non-exchangeable data

Cross-validation (CV) is a popular method for measuring the predictive ability of statistical models, and is often used for model selection. This thesis develops methods for implementing CV on data with dependence structures, like time-series or spatial data. It develops a practical method for computing parallel CV by Markov chain Monte Carlo inference on modern computing hardware. In addition, it analyzes properties of CV estimators for models of time series and spatial data. It finds that the use of certain mathematical evaluation functions are more statistically efficient than other commonly-used approaches.