A Research Of The Prior Distribution Effect On Bayesian Variational Inference Of Erlang Mixture Model

Erlang Mixture Distribution is an important distribution in the field of statistics,and it has important applications in the mixture model.The influence of the prior dis-tribution on the Erlang Mixture Model is considered in this paper.The Erlang Mixture Model is a convex combination of multiple Erlang Distribution,and it has many great properties in the research of many problems.We use the bayesian variational inference to consider the distribution of the Generalized Dirichlet Distribution and Beta-Liouville Distribution respectively as the posterior estimation of the model with the prior distri-bution,and compare the effects of the data fitting.We use the algorithm CMM-VBEM to introduce the process of Erlang Mixture Model in detail from several aspects,includ-ing the initialization of parameters,the adjustment of shape parameters,the selection of mixed number,and the process of posterior distribution estimation.The algorithm CMM is the moment estimation of clustering,and we use it to initialize the parame-ters.The algorithm VBEM is a variational EM algorithm,which is used to estimate the latent variables,shape parameters and mixed weights.Compared with the tradi-tional EM algorithm,the algorithm VBEM can avoid the problem of overfitting data.Finally,the algorithm is verified and compared through data simulation and empirical analysis.Results indicate that,when the sample is small,the choice of the prior distri-bution of Erlang Mixture Model has an influence on the estimation results.And in the example,Beta-Liouville Distribution as prior distribution shows better than Generalized Dirichlet Distribution as prior distribution in model classification.