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Journal: International Journal of Mathematical Research

Abstract: 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. This study contributes in the existing work of Golightly and Wilkinson 2008. Here, we make use of Bayesian argumentation approach on high frequency discretely observed diffusion times. The primary goal, is on the Modified innovation scheme apply to care for sampling degenerating when imputed time is very large.

Arts and Education

International Journal of Mathematical Research

Month: 01-2017 Issue: 1

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