Detection Of Multiple Change Points In Gamma Distributed Sequence Based On RJMCMC

The multiple change points problem is one of the hot research directions which is widely used in finance,medicine,meteorology and other fields.As an important distribution in probability statistics,gamma distribution is closely related to exponential distribution,chisquare distribution and erlang distribution.Data in financial fields such as stock market and actuarial accounting can be well fitted with gamma distribution.Research on such multiple change-point problems has predictive value for identifying economic crisis or important events,which helps people avoid financial risks better.In this paper,the multiple change-point problem of gamma distribution shape parameter is first discussed,and the multiple change-point model of shape parameters is build.We set the prior distribution of the model parameters,and obtain the joint density distribution of the parameters and sample from the likelihood function to explore the full conditional distribution of multiple change-point locations and shape parameters.Four types of jump are designed,and the acceptance probability of each type is give.A reversible jump Markov chain Monte Carlo algorithm is used for determining the number of change points of the model.On the basis,Metropolis-Hastings method is further used to sample the posterior distribution of parameters.Besides,Bayes estimation method is applied to estimating the change point location parameter and shape parameters from sample value.The simulation results and examples of coal mine disasters in Britain show that RJMCMC algorithm is effective for detecting multiple change points of Gamma distribution shape parameters.Then we further extend the algorithm to the multiple change-point model of Gamma distribution double parameters.Five types of jump are designed,and the acceptance probability of each type is give.In the same way,the number of change points of the model is determined by RJMCMC algorithm,and then the Bayesian estimation of each parameter is obtained by combining the M-H sampling method.In order to verify the RJMCMC algorithm,random simulation is carried out.Finally,the algorithm is applied to the data analysis of the successive rises and falls of SSECI yield.The simulation and analysis results show that the RJMCMC based method is efficient in finding multiple change points of gamma distributed sequence.