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

TL;DR

This paper introduces a novel sequential Monte Carlo algorithm for joint inference of reaction rates and latent states in stochastic kinetic models, with applications to modeling and predicting seasonal epidemics.

Contribution

It develops a new particle learning-based method for nonlinear filtering in jump Markov processes, specifically tailored for epidemic modeling.

Findings

Effective inference in epidemic models demonstrated through numerical examples.

Sequential Bayesian estimates enable predictive analysis of epidemic countermeasures.

Algorithm reduces particle degeneracy in continuous-time jump processes.

Abstract

We study sequential Bayesian inference in stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states, modeled as a hidden Markov factor. Using insights from nonlinear filtering of continuous-time jump Markov processes we develop a novel sequential Monte Carlo algorithm for this purpose. Our approach applies the ideas of particle learning to minimize particle degeneracy and exploit the analytical jump Markov structure. A motivating application of our methods is modeling of seasonal infectious disease outbreaks represented through a compartmental epidemic model. We demonstrate inference in such models with several numerical illustrations and also discuss predictive analysis of epidemic countermeasures using sequential Bayes estimates.