Bayesian analysis of the patterns of biological susceptibility via reversible jump MCMC sampling

Abstract

In some biological experiments, it is quite common that laboratory subjects differ in their patterns of susceptibility to a treatment. Finite mixture models are useful in those situations. In this paper we model the number of components and the component parameters jointly, and base inference about these quantities on their posterior probabilities, making use of the reversible jump Markov chain Monte Carlo methods. In particular, we apply the methodology to the analysis of univariate normal mixtures with multidimensional parameters, using a hierarchical prior model that allows weak priors while avoiding improper priors in the mixture context. The practical significance of the proposed method is illustrated with a dose–response data set.