Markov chain Monte Carlo in conditionally Gaussian state space models

A Bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values. A sequence of indicator variables determines which components the errors belong to and the values of the coefficients. The computation is carried out using Markov chain Monte Carlo, with the indicator variables generated without conditioning on the states. Previous approaches use the Gibbs sampler to generate the indicator variables conditional on the states. In many problems, however, there is a strong dependence between the indicator variables and the states causing the Gibbs sampler to converge unacceptably slowly, or even not to converge at all. The new sampler is implemented in O(n) operations, where n is the sample size, permitting an exact Bayesian analysis of problems that previously had no computationally tractable solution. We show empirically that the new sampler can be much more efficient than previous approaches, and illustrate its applicability to robust nonparametric regression with discontinuities and to a time series change point problem.