a b s t r a c t
Inference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely
to appear in smaller models. Our framework allows for many regimes in the transition matrix, without
letting the number of free parameters grow as the square as the number of regimes, but also without
losing a convenient form for the posterior distribution. Calculation of marginal data densities is difficult
in these high-dimensional models. This paper gives methods to overcome these difficulties, and explains
why existing methods are unreliable. It makes suggestions for maximizing posterior density and initiating
MCMC simulations that provide robustness against the complex likelihood shape.