Bayesian Estimation Of Poisson Sequence Parameter Multiple Change Points

The change point model is an important statistical model,and the theoretical research on the change point problem is also widely applied in various fields,so it is a popular direction to study the change point problem.Poisson distribution is a discrete probability distribution commonly used in probability theory.In reality,the frequency of many rare events,such as the annual number of natural disasters in a certain region and the number of mining accidents in a certain country,can be characterized by Poisson distribution.detecting and mastering the occurrence rules of these events can effectively allocate and utilize resources and even reduce economic and property losses.Add the time variable and generalize it to the Poisson process,and Poisson process is an important stochastic process,so the Poisson process parameter change point study for further study of stochastic process lay a foundation.In this paper,bayesian estimation of the change points model of Poisson distribution parameters is firstly carried out.The prior distribution of parameters is set,and the posterior distribution of each parameter is calculated by combining with the likelihood function.The number of change points is confirmed by the RJMCMC algorithm.On the basis of the determination of the number of change points,Markov chain monte carlo method is used to simulate the posterior distribution,and the parameters were estimated according to the stable sample values.Finally,the stochastic simulation and empirical analysis are carried out,and the convergence of the MCMC method is verified by the multi-layer iterative chain and MC error,which shows the effectiveness of the method in estimating change points.Then,based on the data recorded at any time,the double change points of Poisson process parameters are studied.Firstly,the change points model is established,the likelihood function of Poisson process parameter change points model is obtained by introducing potential variables,the conditional posterior distribution of each parameter is calculated by combining the prior information of each parameter,and the posterior distribution is simulated by markov chain monte carlo method,so as to realize the parameter estimation.Finally,The convergence of MCMC method is verified by multi-layer iterative chain and the MC error,and this method is verified by empirical analysis and compared with the results of multiple model selection to prove the effectiveness of this method.