Document Type
Lecture
Publication Date
2-13-2017
Abstract
Partially observed Markov process (POMP) models are ubiquitous tools for modeling time series data in many fields including statistics, econometrics, ecology, and engineering. Because of incomplete measurements and possibly weakly identifiable parameters, making inferences on POMP models can be challenging. Standard methods for inference (e.g., maximum likelihood) with restrictive assumptions of linear Gaussian models have often led to unsatisfactory results when the assumptions are violated. To relax these assumptions, this talk develops a class of simulation-based algorithms called iterated filtering and smoothing for POMP models. First, a novel filter called Bayes map iterated filtering is introduced. This filter recursively combines parameter perturbations with latent variable reconstruction, stochastically optimizing the approximated likelihood of latent variable models and providing an asymptotic guarantee of the performance of this inference methodology. Second, a fast, lightweight algorithm called second-order iterated smoothing is proposed to improve the convergence rate. By exploiting Fisher information as a byproduct of the inference methodology, one can achieve both statistical and computational efficiencies without sacrificing applicability to a general class of models. Finally, the properties of the proposed methodologies are validated through their application to a challenging inference problem of fitting a malaria transmission model with control to time series data, finding substantial gains over current alternatives.
Relational Format
presentation
Recommended Citation
Nguyen, Dao, "Iterated Filtering and Iterated Smoothing Algorithms" (2017). Colloquium. 9.
https://egrove.olemiss.edu/math_colloquium/9
