On Bayesian Analyses and Finite Mixture Models for Proportions

We adopt a Bayesian approach to the analysis of six data sets recording foetal control mortality in mouse litters. We illustrate how a variety of diierent models may be considered, using Markov chain Monte Carlo (MCMC) simulation techniques, and compare the results with the corresponding maximum likelihood analyses. We present an auxiliary variable method for determining the probability that any particular data cell is assigned to a given component in a mixture and we illustrate the value of this approach as a means of interpreting the model parameter representing the overall weight given to any particular component in terms of the observations. Finally, we show how the Bayesian approach provides a natural and unique perspective on the model selection problem via reversible jump MCMC and illustrate how probabilities associated with each of the diierent models may be calculated for each data set. In terms of estimation we show how, by averaging over the diierent models, we obtain reliable and robust inference for any statistic of interest.