Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

Journal Article (Journal Article)

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 regenerating procedure 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 an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Full Text

Duke Authors

Cited Authors

  • Niemi, J; West, M

Published Date

  • June 2010

Published In

Volume / Issue

  • 19 / 2

Start / End Page

  • 260 - 280

PubMed ID

  • 20563281

Pubmed Central ID

  • PMC2887612

Electronic International Standard Serial Number (EISSN)

  • 1537-2715

International Standard Serial Number (ISSN)

  • 1061-8600

Digital Object Identifier (DOI)

  • 10.1198/jcgs.2010.08117


  • eng