Fan, Y.; Leslie, D. S.; and Wand, M. P., Generalised linear mixed model analysis via sequential Monte Carlo sampling, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 20-08, 2008, 20p.
We present a sequential Monte Carlo algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support an extraordinary variety of interesting regression-type analyses, but performing inference is often extremely difficult, even when using the Bayesian approach combined with Markov chain Monte Carlo (MCMC). Sequential Monte Carlo (SMC) is a new and general method for producing samples from posterior distributions. In this article we demonstrate use of the SMC method for performing inference for GLMMs. We demonstrate the effectiveness of the method on both simulated and real data, and find that sequential Monte Carlo is a competitive alternative to the available MCMC techniques.