A1447
Title: Augmented island resampling particle filter for particle MCMC
Authors: Kari Heine - University of Bath (United Kingdom) [presenting]
Abstract: The ability to carry out computations in parallel is paramount to efficient implementations of computationally intensive algorithms. The applicability of the augmented island resampling particle filter (AIRPF) - an algorithm designed for parallel computing - to particle Markov chain Monte Carlo (PMCMC) is investigated. It shows that it produces a non-negative, unbiased estimator of the marginal likelihood, making it suitable for PMCMC. Moreover, the stability results previously shown for the so-called SMC algorithm to cover AIRPF are extended. As a corollary, the error of AIRPF can be bounded uniformly in time by controlling the effective number of filters, which is a diagnostic analogous to the effective sample size. Such control can be implemented by adaptively constraining the interactions between the parallel filters. The superiority of AIRPF over independent bootstrap particle filters is demonstrated not only numerically but also theoretically. In this context, the previously proposed collision analysis approach is extended to derive an explicit expression for the variance of the marginal likelihood estimate and establish an unexpected connection between the filter network topology and the marginal likelihood variance in terms of the Fibonacci sequence.
