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Coupled Conditional Particle Filters
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CoupledCPF

... which stands for Coupled Conditional Particle Filters

This package accompanies the arXiv report https://arxiv.org/abs/1701.02002 "Smoothing with Couplings of Conditional Particle Filters" by Pierre E. Jacob, Fredrik Lindsten, Thomas B. Schön

Functions are provided to construct Rhee--Glynn estimators of smoothing functionals. For comparison, particle filters with fixed-lag and Kalman smoothers are also implemented. Examples include toy auto-regressive models, the classic nonlinear state space model from Gordon, Salmond & Smith 1993, and a prey-predator model with an intractable transition density.

Abstract of the arXiv report:

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.

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