Multiple-order Markov Chain Monte Carlo Sampling Methods with Application to a Changepoint Model

J.A. Stark, W.J. Fitzgerald and S.B.Hladky

Technical Report CUED/F-INFENG/TR 302 (1997), Departments of Engineering and Pharmacology, University of Cambridge.

Markov chain Monte Carlo methods have been applied successfully to a wide variety of modelling problems. There are extra complications when the number of parameters is not fixed. Samplers can be designed that make `reversible jumps' between subspaces that correspond to different orders of a model, but their effectiveness is dependent on a variable transformation. This article explores a number of approaches to the task of formulating moves. A structure is proposed in which moves between subspaces are combined with moves within them. This is especially useful if the latter are of a Gibbs type. Ways of enhancing computational efficiency are considered. A framework is set out for reusing the results of computations in secondary moves once a primary move has been accepted or rejected. These methods are discussed in the context of a model of a piecewise-constant signal which is filtered before the addition of noise. This model was designed with a view to analysing ion channel records.