June 2008
We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerative method to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give examples motivated by applications from systems biology in modelling time series of protein levels in dynamic cellular networks.
Keywords: Bayesian computation; Dynamic non-linear models; Forward filtering, backward sampling; Gaussian sum filter; Markov chain Monte Carlo; Smoothing in state-space models; Non-linear state-space model; Systems biology
Matlab code for examples from the paper, as well as supporting Matlab code for general use in other model contexts, is freely available to interested researchers.