Abstract

Particle filtering methodology is usually applied to non-linear dynamic state space models, but it is possible to adapt the methods to work in static (ie fixed dataset) scenarios. This strategy is advantageous because it combines the best aspects of sequential importance sampling and MCMC . By propagating a swarm of particles across the state space, SMC algorithms are less likely to become trapped in local posterior modes than MCMC , and since it is not necessary to evaluate the full likelihood at each step of the algorithm, a considerable computational saving can also be made.

The class of SMC algorithms of interest in this presentation are those that employ MCMC kernels for particle dynamics, but here, the kernel moves will be made adaptive. The advantage of adaptive over fixed MCMC kernels has been demonstrated in the literature and in particular, adaptation should be advantageous when the posterior is not Gaussian in shape. This presentation will introduce an SMC method that permits MCMC kernel choice and adaptive tuning; the method will be applied to the non-trivial example of Bayesian mixture analysis.