Math Biosci 2021 May 10;335:108583. Epub 2021 Mar 10.
Institut de Biologie de l'ENS (IBENS), Ecole Normale Supérieure, CNRS, INSERM, Université PSL, 75005 Paris, France; International Center for Mathematical and Computational Modeling of Complex Systems (UMMISCO), UMI 209, Sorbonne Université, France; iGLOBE, UMI CNRS 3157, University of Arizona, Tucson, AZ, United States of America.
We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization. This forms the basis of our Data Augmented MCMC, which consists of augmenting parameter space with the unobserved PRM value. Read More