Title: Smoothing with Couplings of Conditional Particle Filters,
Abstract: 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 a realistic
Lotka-Volterra model with an intractable transition density.