Although Bayes estimators are attractive for discrete choice models involving complex non-convex optimization and weak identification, researchers in transportation seem somewhat reluctant to adopt the Bayesian approach. A common argument against simulation-based Bayes estimators is that there are no general rules for assessing convergence. In this thesis, we study convergence of the Markov chain Monte Carlo (MCMC) estimator of logit and probit models, not only in marginal utility (preference) space but also in willingness-to-pay space. We use personal vehicle choice as case study, and we apply a series of convergence diagnostics. Because under regularity conditions the asymptotic distributions of frequentist and Bayes estimators coincide, we also compare the behavior of the posterior first and second moments with that of the point estimates of maximum (simulated) likelihood. When working in preference space, the Bayes estimators converge rather quickly. However, problems appear when analyzing convergence of willingness-to-pay measures that have not been discussed in previous literature. In particular, we observed that.