Negative Binomial And Zero Expansion Models Under Bayes Conditions And Their Applications

There are a large number of count data in many areas of public health, economics, medicine and agriculture. For the analysis of such data, people often use some classic discrete model such as Poisson Model, Negative Binomial model and Generalized Poisson Model. However, in practical problems, data often contains a lot of zero data more than that the standard model can predict. At this point the standard discrete distribution is no longer appropriate to estimate them. In recent years Zero-inflated model has become an effective way to model the data of excess zero. This paper mainly presents the maximum likelihood estimation and Bayesian methods of these models, and focuses on the Bayesian approach of zero-inflated Poisson model.The first chapter presents the main research background. The second chapter introduces the basic theory of Bayesian methods and some processing algorithms. The third chapter introduces the basic concepts of the Poisson model and the negative binomial model,in addition, it analyzes the theory of the Poisson regression and the negative binomial regression under the Bayesian conditions,and the case studies the relationship of the number of visiting doctors for patients and patients’age and their feeling to their physical health, also the paper do the Bayesian estimation to data under a priori assumption. The forth chapter introduces the parameter estimation method of the ZIP model and ZINB model, parameter estimation is simulated on the case of ZIP model, and analyzes the effects of maximum likelihood estimation. And the fishing data is used to analyze parameters in two estimation methods under the ZIP model. The fifth chapter gives the main work of the study. The results show that the Poisson regression and negative binomial regression model are the basic model for count data, but when there is a large proportion of zero data, the estimated consequent of these two models is poor, however, the zero-inflated model can effectively deal with such data. When there is a large sample, the answer to the maximum likelihood estimation is close to Bayesian estimation, but when the number of samples is small, the advantages of the Bayesian approach is displayed, the Bayesian estimation is more meaningful statistically and the result is more accurate. What’s more the Bayesian analysis in the field of zero-inflated model is not deep enough, so it is to be further studied.