Statistical Inference for Discretely Observed Diffusion Epidemic Models

Diffusion processes governed by Stochastic Diffusion Equations (SDEs) are a well known tool for modeling continuous-time data. Consequently, there is widely interest in efficiently estimate diffusion parameters from discretely observed data. Likelihood based inference can be problematic, as the transition densities are rarely available in closed form. One widely used solution proposed by Pedersen (1995) involved the introduction of latent data points between every pair of observations to allow an Euler-Maruyama approximation of the true transition densities to become accurate. Marko Chain Monte Carlo methods are therefore be using to sample the posterior distribution of the latent data and model parameters .We apply the so called method to epidemic data which are discretely observed, that undergo stochastic transition rate. In this case, we introduced a new innovation scheme approach that would explore efficient MCMC schemes that are afflicted by degeneracy problem. The method that capable of sampling efficient estimate of diffusion parameters from discrete observed epidemic data with measurement error.