Twisted particle filters

Abstract

We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from standard algorithms and yet the fluctuation properties of the estimates it provides can be dramatically different. The structure of the optimal transition suggests a new class of algorithms, which we term "twisted" particle filters and which we validate with asymptotic analysis of a more traditional nature, in the regime where the number of particles tends to infinity.

Published in at http://dx.doi.org/10.1214/13-AOS1167 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• The pseudo-marginal approach for efficient Monte Carlo computations
• Recursive Monte Carlo filters: Algorithms and theoretical analysis
• Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms
• Uniform Time Average Consistency of Monte Carlo Particle Filters
• Twisted particle filters

Cited by in corpus (6)

• On Particle Methods for Parameter Estimation in State-Space Models
• On the role of interaction in sequential Monte Carlo algorithms
• Nonlinear System Identification: Learning while respecting physical models using a sequential Monte Carlo method
• Importance sampling type estimators based on approximate marginal MCMC
• Twisted particle filters
• An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models