Bayes WESML Posterior inference from choice-based samples

In this paper I show that the Weighted Exogenous Sampling Likelihood (WESML) estimator for choice-based samples due to Manski and Lerman (1977) can be given a Bayesian interpretation under a multinomial model for the data with improper Dirichlet priors. Bayesian posterior distributions of choice model parameters are computed to study the gains from choice-based sampling and the effect of knowledge of population marginal choice probabilities.