Obiective Bayesian Statistical Inference For Generalized Linear Probability Graph Models

With the rapid development of medical imaging technology in today,magnetic resonance imaging(MRI)and functional magnetic resonance imaging(FMRI)technologies are commonly used in the diagnosis of medical diseases,such as Alzheimer’s disease.Medical researchers generally believe that Alzheimer’s disease is a disorder of the brain.Therefore,it is a key concern of medical researchers to study the functional connectivity network of brain regions in Alzheimer’s disease.The determination of functional connectivity network of brain regions is usually based on the experience of doctors and literature search.This approach lacks to explore the connection network of brain area function based on data analysis,and how to explore the probability graph model of brain functional network based on data is the main problem of this paper.Firstly,by establishing the generalized linear probability graph model,six operators are used to find the essential graph.Secondly,objective Bayesian analysis is used to calculate the marginal likeli-hood of the model so as to select the optimal structure of the probabilistic graph model.Finally,on this basis,the prior distribution,posterior distribution and objective Bayesian estimation of the parameters of the optimal probabilistic graphical model are given.By collecting and sorting FMRI brain imaging data of Alzheimer’s patients and normal people,the ALFF and FALFF index data of 16 brain regions were extracted,and the results of Alzheimer’s disease patients and normal people were explored.The optimal probabilistic graphical model of the sixteen brain regions of normal people,that is,the functional connectivity network of the brain regions,is used to identify the differences in the functional connectivity network of the two groups of people.