Abstract:
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We introduce a set of new Markov chain Monte Carlo (MCMC) algorithms for Bayesian analysis of the multinomial probit model. The multinomial probit model is considered as an appealing discrete choice model in applied research of the social sciences. However, the model is often overlooked because fitting the model can be computationally demanding, owing to the required high-dimensional integrations. Hence, the development of efficient MCMC algorithms has been a topic of recent work and in some cases of much debate. Our Bayesian representation of the model places a new, and possibly improper, prior distribution directly on the identifiable parameters and thus is relatively easy to interpret and use. Our algorithms, which are based on the method of marginal data augmentation, involve only draws from standard distributions and dominate other available Bayesian methods in that they are as quick to converge as the fastest methods, but with a more attractive prior specification. Computer code for our algorithms is publicly available.
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