Abstract
We examine some Markov chain Monte Carlo (MCMC) methods for a generalized non-linear regression model, the Logit model. It is first shown that MCMC algorithms may be used since the posterior is proper under the choice of non-informative priors. Then two non-standard MCMC methods are compared: a Metropolis–Hastings algorithm with a bivariate normal proposal resulting from an approximation, and a Metropolis–Hastings algorithm with an adaptive proposal. The results presented here are illustrated by simulations, and show the good behavior of both methods, and superior performances of the method with an adaptive proposal in terms of convergence to the stationary distribution and exploration of the posterior distribution surface.