USING PARALLEL PARTICLE FILTERS FOR INFERENCES IN HIDDEN MARKOV MODELS

Abstract

In this thesis, we use particle filters on segmentations of the latent-state sequence of a hidden Markov model, to estimate the model likelihood and distribution of the hidden states. Under this set-up, the latent-state sequence is partitioned into subsequences, and particle filters are applied to provide estimation for the entire sequence. An important advantage is that parallel processing can be employed to reduce wall-clock computation time. We use a martingale difference argument to show that the model likelihood estimate is unbiased. We show, on numerical studies, that the estimators using parallel particle filters have comparable or reduced (for smoothed hidden-state estimation) variances compared to those obtained from standard particle filters with no sequence segmentation. We also illustrate the use of the parallel particle filter framework in the context of particle MCMC, on a stochastic volatility model.