期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2015
卷号：112
期号：3
页码：719-724
DOI：10.1073/pnas.1410597112
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：SignificanceMany scientific challenges involve the study of stochastic dynamic systems for which only noisy or incomplete measurements are available. Inference for partially observed Markov process models provides a framework for formulating and answering questions about these systems. Except when the system is small, or approximately linear and Gaussian, state-of-the-art statistical methods are required to make efficient use of available data. Evaluation of the likelihood for a partially observed Markov process model can be formulated as a filtering problem. Iterated filtering algorithms carry out repeated Monte Carlo filtering operations to maximize the likelihood. We develop a new theoretical framework for iterated filtering and construct a new algorithm that dramatically outperforms previous approaches on a challenging inference problem in disease ecology. Iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with latent variable reconstruction. Previously, theoretical support for these algorithms has been based on the use of conditional moments of perturbed parameters to approximate derivatives of the log likelihood function. Here, a theoretical approach is introduced based on the convergence of an iterated Bayes map. An algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed Markov process.
关键词：sequential Monte Carlo ; particle filter ; maximum likelihood ; Markov process
