Bayesian Inference of the Stochastic Gompertz Growth Model for Tumor Growth

Abstract

Abstract A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leadingcause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations wouldbe possible based on the continuous path likelihood on condition that a continuous sample path of the processis recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous recordor infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except afew special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method ofparameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that isapplicable for several data structures. We compared a Markov transition data structure with a data structure thathave an initial point.Keywords: Stochastic diffusion. Gompertz growth model, tumor growth, Bayesian, Markov datastructure, sparse data structure.