Markov Chain Monte Carlo-Based Bayesian Analysis of Binary Response Regression, with Illustration in Dose-Response Assessment

This paper deals with the Bayesian analysis of binary response regression using Markov chain Monte Carlo (MCMC) methods, more specifically the Metropolis sampler, for posterior simulation. The methodology is illustrated with real-world data from a bioassay experiment. Inference about quantities of typical interest in the dose-response setting such as the lethal dose is discussed as well. MCMC are routinely implemented through popular Bayesian software such as Win-/Open-BUGS. However, these remain black boxes which provide no insight in the estimation procedure. This paper exemplifies that developing and implementing an MCMC sampler may, in many practical situations, be relatively straightforward. The R code for the Metropolis sampler is also provided in an appendix to the paper