Bayesian inference and model comparison for random choice structures

We complete the development of a testing ground for axioms of stochastic discrete choice, begun in McCausland and Marley (2013). Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced in that paper. These priors are joint distributions over various discrete choice distributions on choice sets of different sizes. Choice distributions over different choice sets can be mutually dependent, so the priors are not in general conjugate; this calls for new Markov chain Monte Carlo posterior simulation methods. We demonstrate the methods by analysing data from a previously reported experiment and report the resulting evidence for and against various axioms.