The Properties Of The Generalized Bartlett Graph And Its Bayesian Inference

In recent years,the Bayesian inference on the graph model has received high attention in the literature.As is known to all,the decomposable graphs has special attribute,that makes the Bayesian inference on the decomposable graphs is much easier to handle than the general undecomposable graphs.In this paper,for Bayesian infeerence on the graph model selection,we first study the generalized Bartlett graphs.The properties of the generalized Bartlett graphs are studied by the proposed decomposable covering algorithm.Generalized Bartlett graphs contain decomposable graphs such as a special case,but it is much larger than the range of decomposable graphs.This provides a flexible modeling framework for Bayesian inference.Secondly,G-Wishart distribution and generalized G-Wishart distribution based on graphical model are studied for the selection of distribution family in the process of Bayesian inference.The generalized G-Wishart distribution with multiple shape parameters can be applied flexibly to Bayesian inference.Finally,in view of the sampling problem in the process of Bayesian inference,we introduce the Gibbs sampling method based on graphical model.Using Gibbs sampling algorithm,we can obtain a posterior distribution from a generalized Bartlett graph from the generalized G-Wishart distribution.This allows the sampling of complex functions to be implemented.Using Generalized Bartlett graphs,generalized G-Wishart distribution and Gibbs sampling algorithm,the calculation of normalized constants in the complex graph model is solved.That enables the Bayesian inference process on the generalized Bartlett graphs to be realized.