Bayesian inference of binary regression models with parametric link

A computationally tractable Bayesian inference for binary regression models with parametric link is derived utilizing a Markov chain Monte Carlo algorithm to simulate from the joint posterior distribution of the regression and the link parameter. In particular, Bayesian posterior calculations are faciltated for a generalized probit regression model involving tail modification by developing a hybrid sampling algorithm with Gibbs and Metropolis/rejection sampling steps. It also involves sufficiency and other reduction arguments to optimize the algorithm. The proposed algorithm is applied to two examples producing marginal and joint posterior density estimates for link and regression parameters. Bayesian point and interval estimates for these parameters as well as for the corresponding success probabilities are also investigated.