Bayesian Parameter Estimation Of Finite Mixture Erlang Model

In recent years,Bayesian analysis of mixture models with unknown number of components can be performed using methods such as Dirichlet process mixtures,distributional distances,RJMCMC algorithm,BDMCMC algorithm.Bayesian mixture models are popular in many disciplines,such as econometrics,machine learning,epidemiology,and biological sequence analysis.Among them,RJMCMC algorithm has been widely used in the mixture of Gaussian distributions,the mixture of Gamma distributions,the mixture of Erlang distributions and so on.While BDMCMC algorithm has been used in the mixture of Gaussian distributions,the mixture of Gamma distributions and so on.In this paper,BDMCMC algorithm is applied to the finite mixture of Erlang distributions to estimate the parameters of the finite mixture Erlang model with common rate parameter,the number of components k is unknown but finite.Firstly,the BDMCMC algorithm is combined with handling label switching issues to estimate the number of components k;Then determine the estimated values of each parameter:average the weight parameters and rate parameter to get their estimated values separately and round the means of the shape parameters to get their estimated values.The experimental simulation is mainly divided into two parts.The first part is to analyze the data that the real distribution is mixture of Erlang distributions,including parameters estimation of two-component,three-component and four-component mixture Erlang models;The second part is to analyze the data of real distribution which is not mixture of Erlang distributions,and estimates the parameters of log-normal distribution of one component and truncated Gaussian distributions of two components respectively.All show that the finite mixture Erlang model with common rate parameter can fit the data well.In the case study,this model is used to fit the data:waiting time between eruptions for the Old Faithful Geyser,and the results are compared with those of Richardson&Green(1997).The model in this paper is simple and easy to implement,and is suitable for data sets with large differences in components.