This paper adopts an approach based on the concepts of random utility maximization and builds on the general theoretical framework of Lancaster and on the conceptual and econometric innovations of McFadden. Recent research in this area explores models that account for context effects, as well as methods for characterizing heterogeneity, response variability and decision strategy selection by consumers. This makes it possible to construct much richer empirical models of individual consumer behavior. A Bayesian approach provides a useful way to estimate and interpret models that are difficult to accomplish by conventional maximization/minimization algorithms. The application reported in the paper involves analysis of reference dependence and product labeling as context effects and the assessment of heterogeneity and response variability.