Traditional criteria for comparing alternative Bayesian hierarchical models,
such as cross validation sums of squares, are inappropriate for non-standard
data structures. More flexible cross validation criteria such as predictive
densities facilitate effective evaluations across a broader range of data
structures, but do so at the expense of introducing computational challenges.
This paper considers Markov Chain Monte Carlo strategies for calculating
Bayesian predictive densities for vector measurements subject to differential
component-wise censoring. It discusses computational obstacles in Bayesian
computations resulting from both the multivariate and incomplete nature of the
data, and suggests two Monte Carlo approaches for implementing predictive
density calculations. It illustrates the value of the proposed methods in the
context of comparing alternative models for joint distributions of contaminant
concentration measurements.
Keywords: cross validation, data augmentation, predictive
density, marginal density, nested integration