Maximum Likelihood Estimation for Partially Observed Markov Model Using Different Tail Perturbations
Date of Award
1-1-2025
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
First Advisor
Dao Nguyen
Second Advisor
Sandra Spiroff
Third Advisor
Hailin Sang
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
This work is about parameter estimation of POMP models using the two-time scale Iterated Filtering algorithms with p-generalized Gaussian perturbations. The algorithms are effective for estimating numerous types of infectious disease models such as COVID-19, influenza or various other diseases. First, we introduce the generalization of Stein’s identity for normal distribution to p-generalized Gaussian distribution, which enables more flexible perturbation with different tail behaviors. Then, we provide proofs and verify their authenticity by applying them in black box optimization as well as optimization of multivariate state space models. Also, we propose a novel weighted average algorithm for maximizing likelihood through the two-time-scale stochastic approximation. We integrate the algorithm into iterated filtering framework, relaxing the requirement for a bounded variance of the two-timescale stochastic approximation. Initially, p-generalised Gaussian smoothing is combined with Weighted Average Iterated filtering in two toy problems: a linear ou2 model and a nonlinear gompertz model. Subsequently, the potential of this technique is demonstrated in fitting two real POMP examples: cholera and our fully designed COVID-19 models, incorporating a highly nonlinear structure with discrete population dynamics, seasonality, and extra-demographic stochasticity.
Recommended Citation
Qazi, Zamzam, "Maximum Likelihood Estimation for Partially Observed Markov Model Using Different Tail Perturbations" (2025). Electronic Theses and Dissertations. 3365.
https://egrove.olemiss.edu/etd/3365