Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling

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Abstract
Constrained parameter problems arise in a wide variety of applications, including bioassay, actuarial graduation, ordinal categorical data, response surfaces, reliability development testing, and variance component models. Truncated data problems arise naturally in survival and failure time studies, ordinal data models, and categorical data studies aimed at uncovering underlying continuous distributions. In many applications both parameter constraints and data truncation are present. The statistical literature on such problems is very extensive, reflecting both the problems’ widespread occurrence in applications and the methodological challenges that they pose. However, it is striking that so little of this applied and theoretical literature involves a parametric Bayesian perspective. From a technical viewpoint, this perhaps is not difficult to understand. The fundamental tool for Bayesian calculations in typical realistic models is (multidimensional) numerical integration, which often is problem...

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