Unbiased Smoothing using Particle Independent MetropolisHastings
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Proceedings of Machine Learning Research, PMLR 89:23782387, 2019.
Abstract
We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent MetropolisHastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to offtheshelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévydriven stochastic volatility model and a stochastic kinetic model.
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