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Title: Multilevel bootstrap particle filter Authors:  Daniel Burrows - University of Bath (United Kingdom) [presenting]
Abstract: Multilevel Monte Carlo (MLMC) was introduced at the turn of the millennium, and it has since become popular, particularly in the field of financial mathematics as a means to avoid expensive solving of stochastic differential equations. We develop MLMC in the context of sequential Monte Carlo (SMC) to obtain a novel multilevel bootstrap particle filter (MLBPF). SMC methods are often the only feasible way to estimate the distribution of a partially observed latent Markov process. We consider situations where the evaluation of the particle weights, i.e. the likelihood, is too expensive to make the standard bootstrap particle filter (BPF) feasible for large sample sizes. We adopt the multilevel approach whereby a substantially less expensive likelihood approximation is used for the bulk of particles, and the resulting bias due to the approximation is then corrected by a relatively small number of expensive evaluations of the exact likelihood. As a result, we obtain an approximation accuracy comparable to BPF, but at a lower computational cost. We establish the strong law of large numbers and central limit theorem for MLBPF and demonstrate its performance on numerical applications.