Sequential Bayesian Inference in Hidden Markov Stochastic Kinetic Models with Application to Detection and Response to Seasonal Epidemics

• Activity Number: 134
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Junjing Lin*+ and Michael Ludkovski
• Companies: Univeristy of California, Santa Barbara and University of California, Santa Barbara
• Keywords: Bayesian computation ; sequential Monte Carlo ; particle learning ; hidden Markov models ; online algorithms

Abstract

We develop a novel sequential Monte Carlo (SMC) algorithm based on Particle Learning (PL), aiming to jointly infer parameters and latent factors in continuous-time hidden Markov models. The data of interest are in general strongly seasonal, yet noisy and fluctuating. In order to examine the underlying dynamics, we utilize the analytical jump Markov structure and perform sequential Bayesian inference when the joint likelihoods of the unknowns are not of closed form. Compared to some other SMC methods, our approach shows advantages in alleviating particle degeneracy as well as controlling computational errors for the applications we consider. In the examples of flu detection, the parameter estimates converge to the true values quickly as data accumulate; furthermore, the estimated posteriors closely track the flu seasons and can be successfully used for real-time policy making to mitigate the outbreaks.