Backward importance sampling for partially observed diffusion processes
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This paper proposes a new Sequential Monte Carlo algorithm to perform maximum likelihood estimation in partially observed diffusion processes. Training such generative models and obtaining low variance estimators of the posterior distributions of the latent states given the observations is challenging as the transition densities of the latent states cannot be evaluated pointwise. In this paper, a backward importance sampling step is introduced to estimate such posterior distributions instead of the usual acceptance-rejection approach. This allows to use unbiased estimates of the unknown transition densities available under mild assumptions for multivariate stochastic differential equations while acceptance-rejection based methods require strong conditions to obtain upper-bounded estimators. The performance of this estimator is assessed in the case of a partially observed stochastic Lotka-Volterra model.
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