Bayesian Parameter Estimation Of Univariate Mixture Erlang Model Based On Censored Data

The data generated in various fields in the era of big data is becoming increasingly complex.Data in the fields of medical biology,public health,financial insurance,reliability engineering and environmental monitoring studies are censored due to reasons such as measurement equipment,experimental design,and data collection schemes.This paper generalizes the univariate mixture Erlang model to the parameter estimation problem of censored data(UMEMC).This paper reasonably selects the prior distribution of parameters,introduces two latent variables,calculates the full-condition posterior distribution of each model parameter,and further designs a flexible MCMC algorithm to complete the parameter estimation.The innovation of the algorithm mainly lies in the processing of censored data as latent variables.The range of the observation period is[CL,CR],this article only considers that the data on the left side of the fixed value CL or the right side of CR has been censored.Therefore,when the data is left censored,it is sampled from the lefttruncated Erlang distribution corresponding to the first mixed component identified from the UMEMC model.When the data is right-censored,it is sampled from the righttruncated Erlang distribution of the last mixed component.The y sample extracted with the Gibbs algorithm makes up for the censored data information to a certain extent.Compared with the data information which directly ignores the censored data,a more accurate and reasonable parameter estimation result can be obtained.The UMEMC model is applied to two-component left-censored,three-component both-censored,four-component right-censored,left-censored generalized Pareto distribution simulation data,and left-censored RNA virus load data set UTIdata.It is verified that the model can more accurately and effectively fit such data with multipeak,off-peak,long-tailed characteristics,censored.