An objective Bayesian estimation of parameters in a log-binomial model

Log-binomial model is commonly recommended for modeling prevalence ratio just as logistic regression is used to model log odds-ratio. However, for the log-binomial model, the parameter space turns out to be restricted causing difficulties for the maximum likelihood estimation in terms of convergence of numerical algorithms and calculation of standard errors. Bayesian approach is a natural choice for modeling log-binomial model as it involves neither maximization nor large sample approximation. We consider two objective or non-informative priors for the parameters in a log-binomial model: an improper flat prior and a proper prior. We give sufficient conditions for the posterior from the improper flat prior to be proper, and compare the two priors in terms of the resulting posterior summaries. We use Markov Chain Monte Carlo via slice sampling to simulate from the posterior distributions.