Bayesian Modeling And Inference Of Meta-Data

With the advent of the era of big data,the updating of data is getting faster and faster.Different people will continue to do research on the same problem.This will produce a lot of data and conclusions.These results are often different.How do researchers judge which one is the correct? Meta-analysis is put forward in this case.It is a statistical analysis method that summarizes the results obtained by different researchers under the same topic after researching them.In recent years,this idea has been widely used in the fields of natural sciences such as medicine and biology.Among them,medicine is the most common and has been well received in the industry.Scientists hope to use the data as much as possible in a scientific way to obtain more objective results.This is the main idea of meta-analysis.When performing meta-analysis,we first need to summarize the information.The collected data is meta-data.Bayesian statistical method is a relatively mature and widely used inference method.Because it combines sample information and prior information,it is sought after by researchers at home and abroad.The topic of the relationship between the characteristics of organisms and their allometric growth has always been a topic of concern to biologists,because it is related to the activities and functions of organisms,and metabolism is one of the indispensable behaviors of organisms.The impact is worth noting.This paper addresses the practical issue of the impact of plant population density on metabolic rate,meta analysis and Bayesian statistical methods are combined.First,a random coefficient regression model based on meta data is established,and Bayesian statistical methods are used for inference.The sampling method determines the final parameters of the model.This model can be applied to the analysis of most meta data.It is widely used and has good development prospects.This paper is divided into four chapters.The first chapter is the introduction,mainly introducing meta analysis and Bayesian statistical methods.The second chapter is the establishment of the model.It analyzes the meta data collected by different people in different years on the practical problem of the impact of plant population density on plant metabolic rate.For this problem,we established a random coefficient regression model and used Bayesian statistical methods to statistically infer its parameters.According to the prior distribution of the parameters and thelikelihood function of the data variables,the posterior distribution of the parameters is obtained,and the Gibbs sampling method in the Markov chain Monte Carlo method(MCMC method)is used for sampling to obtain the estimated values of the parameters.Then the basic theory of Gibbs sampling method and variance ratio is introduced.The third chapter is data analysis.In view of the actual problems and models established,we use R language software to program,and then sample the posterior distribution of the estimated parameters to obtain the estimated values of the parameters.For the performance of the Markov chain,we use the variance ratio to judge the degree of fit,and verify the sensitivity of the sampling results to the initial value by changing the initial value.In the last chapter,we summarize and look forward to the problems.