MCMC Strategies for Computing Bayesian Predictive Densities for Censored Multivariate Data

• Published in: Journal of computational and graphical statistics Vol. 14; no. 2; pp. 395 - 414
• Main Authors: Lockwood, J. R, Schervish, Mark J
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.06.2005; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Censored data; Censorship; Comparative studies; Coordinate systems; Cross-validation; Data augmentation; Density estimation; Estimation methods; Marginal density; Markov analysis; Mathematical models; Mathematical vectors; Modeling; Monte Carlo simulation; Multivariate analysis; Nested integration; Parametric models; Predictive modeling; Spatial models
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1198/106186005X47967

Traditional criteria for comparing alternative Bayesian hierarchical models, such as cross-validation sums of squares, are inappropriate for nonstandard 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 article 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.