Iterated filtering

TL;DR

This paper develops new theoretical results on the convergence of iterated filtering algorithms used for inference in partially observed Markov process models, supported by empirical evidence of their effectiveness.

Contribution

It introduces a new recursive approach for likelihood maximization via importance sampling and establishes convergence theory for iterated filtering algorithms.

Findings

Convergence of iterated filtering algorithms is theoretically supported.

A new recursive likelihood maximization method is proposed.

Iterated importance sampling is introduced as a special case.

Abstract

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growing body of empirical evidence that iterated filtering algorithms provide an effective inference strategy for scientific models of nonlinear dynamic systems. The first step in our theory involves studying a new recursive approach for maximizing the likelihood function of a latent variable model, when this likelihood is evaluated via importance sampling. This leads to the consideration of an iterated importance sampling algorithm which serves as a simple special case of iterated filtering, and may have applicability in its own right.