Iterated filtering
Edward L. Ionides, Anindya Bhadra, Yves Atchadé, Aaron King
The Annals of Statistics · 2011 · Volume 39 · Issue 3
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.
Keywords
62M09, Dynamic systems, Filtering, importance sampling, partially observed Markov process, sequential Monte Carlo, state space model
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