Bayesian Analysis Of Mixed Growth Models Defined By SDE

Since the1940s, the model of animal growth has been widely studied and hasbeen widely used in biological genetics, pediatrics, cancer cell growth and tumor cellgrowth in other areas. With further research, the parameter estimation of stochasticmixed effect growth model evoke more and more attention. the Bayesian estimationof parameter of Gompertz mixed effects model are studied. this article will present theLogistic，Richards mixed effects model’s parameter estimation.The main work: Obtain the parameter estimation of Logistic mixed effects modeland Richards mixed effects model, and achieve the parameter estimation of the abovethree mixed effects growth model on Matlab. For parameters with explicit form,obtained directly from the estimation formula, the other, we simulated its estimationby using the EM algorithm, MCMC algorithm. Finally, the numerical experimentshows that parameter estimation results were significant.This thesis is divided into four chapters. Chapter1briefly introduces the basicconcept of mixed effects model and linear mixed effects model, nonlinear mixedeffects model, the stochastic mixed effects model based on stochastic differentialequation and four kinds of growth model and its main characteristics. Chapter2introduces the Bayesian estimation method, the EM algorithm, MCMC algorithm.Chapter3obtains the Logistic，Richards mixed effects model’s parameter estimation,For parameters with no explicit form, simulated its estimated value by using the EMalgorithm, MCMC algorithm. Chapter4summarizes the full text content andinnovation points and deficiencies.