基于RJMCMC算法的Gamma分布形状参数多变点检测  

Detection of Multiple Change-points in the Scale Parameter of Gamma Distributed Sequence Based on Reversible Jump MCMC Algorithm

作　　者：程慧慧 许淑月 CHENG Huihui;XU Shuyue(School of Mathematics and Statistics,North China University of Water Conservancy and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2022年第4期1-9,共9页Journal of Henan Institute of Education(Natural Science Edition)

摘　　要：首先建立Gamma分布形状参数多变点模型,给出该分布模型的似然函数,得到变点位置和形状参数的满条件分布。基于可逆跳跃马尔可夫链蒙特卡洛(RJMCMC)算法确定该模型的变点个数,进一步利用马尔可夫链蒙特卡洛(MCMC)方法对参数的满条件分布进行抽样,并利用贝叶斯估计方法得到变点位置和形状参数的估计值。仿真模拟和英国煤矿灾害实例均表明了RJMCMC算法结合MCMC算法对Gamma分布形状参数多变点检测的有效性。To detect the problem of Gamma distribution shape parameter change point,the change-point model of Gamma distribution shape parameters is established and then the likelihood function of the change-point model is given to explore the full conditional distribution of the change-point location and shape parameters.RJMCMC algorithm is used for determining the number of change points of the model and MCMC method is further used to sample the full conditional distribution of the parameters.Besides,Bayes estimation method is applied to estimate the change point location parameter and shape parameters.The simulation results and examples of coal mine disasters in Britain show that RJMCMC algorithm combined with MCMC algorithm is effective for detecting multiple change points of Gamma distribution shape parameters.

关 键 词：GAMMA分布 变点 后验分布 贝叶斯估计 RJMCMC 

分 类 号：O212[理学—概率论与数理统计]