A Bayesian approach to finite mixture models in bioassay via data augmentation and Gibbs sampling and its application...

After continued treatment with an insecticide, within the population of the susceptible insects, resistant strains will occur. It is important to know whether there are any resistant strains, what the proportions are, and what the median lethal doses are for the insecticide. Lwin and Martin (1989, Biometrics 45, 721-732) propose a probit mixture model and use the EM algorithm to obtain the maximum likelihood estimates for the parameters. This approach has difficulties in estimating the confidence intervals and in testing the number of components. We propose a Bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and Gibbs sampler. We use Bayes factor for model selection and determining the number of components. We illustrate the method with data published in Lwin and Martin (1989).