Data-driven particle Filters for particle Markov Chain Monte Carlo

This paper proposes new automated proposal distributions for sequential Monte Carlo algorithms, including particle filtering and related sequential importance sampling methods. The wrights for these proposal distributions are easily established, as is the unbiasedness property of the resultant likelihood estimators, so that the methods may be used within a particle Markov chain Monte Carlo (PMCMC) inferential setting. Simulation exercises, based on a range of state space models, are used to demonstrate the linkage between the signal-to-noise ratio of the system and the performance of the new particle filters, in comparison with existing filters. In particular, we demonstrate that one of our proposed filters performs well in a high signal-to-noise ratio setting, that is, when the observation is informative in identifying the location of the unobserved state. A second filter, deliberately designed to draw proposals that are informed by both the current observation and past states, is shown to work well across a range of signal-to noise ratios and to be much more robust than the auxiliary particle filter, which is often used as the default choice. We then extend the study to explore the performance of the PMCMC algorithm using the new filters to estimate the likelihood function, once again in comparison with existing alternatives. Taking into consideration robustness to the signal-to-noise ratio, computation time and the efficiency of the chain, the second of the new filters is again found to be the best-performing method. Application of the preferred filter to a stochastic volatility model for weekly Australian/US exchange rate returns completes the paper.