Journal
ANNALS OF STATISTICS
Volume 39, Issue 3, Pages 1776-1802Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AOS886
Keywords
Dynamic systems; sequential Monte Carlo; filtering; importance sampling; state space model; partially observed Markov process
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Funding
- NSF [DMS-08-05533, EF-04-30120, DEB-0553768]
- Graham Environmental Sustainability Institute
- Science & Technology Directorate, Department of Homeland Security
- Fogarty International Center, National Institutes of Health
- University of California, Santa Barbara
- State of California
- Direct For Mathematical & Physical Scien [0805533] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0805533] Funding Source: National Science Foundation
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Inference for partially observed Markov process models has been a long-standing 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.
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