Unbiased Smoothing using Particle Independent Metropolis-Hastings
This addresses the smoothing problem in statistics and machine learning, offering an easier-to-implement unbiased method for parallel computing and confidence intervals, though it is incremental as it builds on existing MCMC and particle filter techniques.
The paper tackles the bias in finite-time smoothing estimators for latent Markov processes by proposing a coupling method for Particle Independent Metropolis-Hastings chains to produce unbiased estimators, which is demonstrated on stochastic volatility and kinetic models.
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 Metropolis-Hastings (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 off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.