Efficient Bayesian Inference for Dynamic Mixture Models

Abstract

A Bayesian approach is presented for estimating a mixture of linear Gaussian state-space models. Such models are used to model interventions in time series and nonparametric regression. Markov chain Monte Carlo sampling is usually necessary to obtain the posterior distributions of such mixture models, because it is difficult to obtain them analytically. The methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently implement a Markov chain Monte Carlo sampling scheme that converges rapidly to the posterior distribution. The methodology is illustrated by fitting an autoregressive model subject to interventions to zinc concentration in sludge.

Key Words:

• Level shifts
• Markov chain Monte Carlo
• Mixture of normals
• Outliers
• State-space model