Bayesian Data Augmentation for Partially Observed Stochastic Compartmental Models

Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic considered more realistic, yet complicated to estimate due missing data. In this paper we present a novel algorithm for estimating Susceptible-Infected-Recovered and Susceptible-Exposed-Infected-Recovered (SIR/SEIR) epidemic model within Bayesian framework, which can be readily extended complex models. Specifically, based on infinitesimal conditional independence properties model, able find proposal distribution Metropolis is very close correct posterior distribution. particular, it acts as good unknown number events, such infected individuals. Finding has historically been difficult problem. As consequence, rather than perform step updating one data point at time, have single entire set observations. A real illustrations necessary mathematical theory supporting our results presented.