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

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 wha t the median lethal doses are for the insecticide. Lwin and Martin (1989, B iometrics 45, 721-732) propose a probit mixture model and use the Ehl algor ithm to obtain the maximum likelihood estimates for the parameters. This ap proach has difficulties in estimating the confidence intervals and in testi ng the number of components. We propose a Bayesian approach to obtaining th e credible intervals for the location and scale of the tolerances in each c omponent and for the mixture proportions by using data augmentation and Gib bs sampler. We use Bayes factor for model selection and determining the num ber of components. We illustrate the method with data published in Lwin and Martin (1989).