Bayesian inference for a susceptible-exposed-infected-recovered epidemic model with data augmentation

Abstract

ABSTRACT A Bayesian data-augmentation method allows estimating the parameters in a susceptible-exposed-infected-recovered (SEIR) epidemic model, which is formulated as a continuous-time Markov process and approximated by a diffusion process using the convergence of the master equation. The estimation was carried out with latent data points between every pair of observations simulated through the Euler-Maruyama scheme, which involves imputing the missing data in addition to the model parameters. The missing data and parameters are treated as random variables, and a Markov-chain Monte-Carlo algorithm updates the missing data and the parameter values. Numerical simulations show the effectiveness of the proposed Markov-chain Monte-Carlo algorithm.