Inference for dynamic and latent variable models via iterated, perturbed Bayes maps

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 112; no. 3; pp. 719 - 724
• Main Authors: Ionides, Edward L., Nguyen, Dao, Atchadé, Yves, Stoev, Stilian, King, Aaron A.
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 20-01-2015; National Acad Sciences
• Subjects: Algorithms; Approximation; Bayes Theorem; Bayesian analysis; Biological Sciences; Cholera - epidemiology; Cholera - transmission; Humans; Likelihood Functions; Markov analysis; Models, Theoretical; Optimization algorithms; Parameter optimization; Physical Sciences; Stochastic models; Markov process; sequential Monte Carlo; particle filter; maximum likelihood
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1410597112

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.
Significance Many 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.