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Smoothing with Couplings of Conditional Particle Filters

Version 5 2023-08-16, 17:22
Version 4 2021-09-15, 14:24
Version 3 2020-08-24, 08:43
Version 2 2019-04-30, 14:50
Version 1 2019-03-21, 14:16
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posted on 2019-03-21, 14:16 authored by Pierre E. Jacob, Fredrik Lindsten, Thomas B. Schön

In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and confidence intervals can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly-informative observations, and for a realistic Lotka-Volterra model with an intractable transition density.

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