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Title: Limit theorems for sequential MCMC methods Authors:  Axel Finke - National University of Singapore (Singapore) [presenting]
Adam Johansen - University of Warwick (United Kingdom)
Arnaud Doucet - University of Oxford (United Kingdom)
Abstract: Both \emph{sequential Monte Carlo (SMC)} methods (``particle filters'') as well as \emph{sequential MCMC} methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to an MCMC kernel. The latter have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish a strong law of large numbers and a central limit theorem for sequential MCMC methods. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.