Lookahead Strategies for Sequential Monte Carlo

Abstract

Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with which future information can help sharpen the inference about the current state. By providing theoretical justification of several existing algorithms and introducing several new ones, we study systematically how to construct efficient SMC algorithms to take advantage of the "future" information without creating a substantially high computational burden. The main idea is to allow for lookahead in the Monte Carlo process so that future information can be utilized in weighting and generating Monte Carlo samples, or resampling from samples of the current state.

Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Limit theorems for sequential MCMC methods
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• Inference Trees: Adaptive Inference with Exploration
• Bayesian inference for Markov jump processes with informative observations
• Sequential Monte Carlo with Highly Informative Observations
• Cluster Prediction for Opinion Dynamics from Partial Observations
• Replica Conditional Sequential Monte Carlo
• $k$-means: Fighting against Degeneracy in Sequential Monte Carlo with an Application to Tracking
• Improved Particle Filters for Vehicle Localisation
• Efficient convergence through adaptive learning in sequential Monte Carlo Expectation Maximization