title: Inference for dynamic and latent variable models via iterated, perturbed Bayes maps.
abstract: 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.
authors.affiliation: Departments of Statistics, ionides@umich.edu.
authors.forename: Edward L
authors.initials: EL
authors.lastname: Ionides
authors.affiliation: Departments of Statistics.
authors.forename: Dao
authors.initials: D
authors.lastname: Nguyen
authors.affiliation: Departments of Statistics.
authors.forename: Yves
authors.initials: Y
authors.lastname: Atchadé
authors.affiliation: Departments of Statistics.
authors.forename: Stilian
authors.initials: S
authors.lastname: Stoev
authors.affiliation: Ecology and Evolutionary Biology, and Mathematics, University of Michigan, Ann Arbor, MI 48109.
authors.forename: Aaron A
authors.initials: AA
authors.lastname: King
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D002771:Cholera / Q000453:epidemiology / Q000635:transmission; D006801:Humans; D016013:Likelihood Functions; D008962:Models, Theoretical
keywords: Markov process; maximum likelihood; particle filter; sequential Monte Carlo