A Study On Parameter Estimation And Model Selection Based On Approximate Bayesian Computation

Being one of the most important branches of statistical studies,Bayesian statistical inference method has been applied in various research fields.In the process of Bayesian statistical inference,how to select and calculate the likelihood function is the key question.Particularly,with the continuous development of statistical models in the field of biological mathematics,the likelihood functions of models become more and more complex and it is often hard to obtain analytical expressions or to be calculated.Therefore,it is difficult to deal with Bayesian inference due to the complexity of likelihood functions.At this stage,approximate Bayesian computation(ABC)can be applied to solve the problem.In this work,we will discuss the approximate Bayesian computation thoroughly from three aspects,namely,the theoretic analyses,algorithm designs and practical applications.Based upon the detailed comparisons between various algorithms,we have proposed a novel algorithm that helps with model selections based on the particle filtering and Monte Carlo method.And it has been applied to the model selection problem for SIR models,which reveals some good results.The overall contents of this work are as follows:1.Descriptions of the basic principle of approximate Bayesian computation and the selection of the summary statistics and the definition of tolerance threshold during the realization;2.Descriptions of the basic ABC rejection algorithm,ABC regression algorithm,ABC-MCMC algorithm based on MCMC method,ABC-PRC algorithm based on particle filtering,ABC-PMC algorithm,ABC-SMC algorithm and comparisons between these algorithms;3.Descriptions of the proposed ABC-PMC model selection algorithm based on particle filter and Monte Carlo method;4.Applied examples in parameter estimation and model selection: a binomial distributed model,a Poisson distributed model,an influenza virus infection model and a classical infectious disease model.