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

Abstract

In this paper, the multiple change-point problem in the scale parameter of a sequence of independent gamma distributed observations is discussed. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is developed to compute the posterior probabilities of the number and positions of the multiple change-points. Four types of jumps are designed, and the acceptance probability of each type is given. The simulation studies show that the RJMCMC-based method is efficient in the detection of multiple change-points in the scale parameter in gamma distributed sequence, and performs better than a self-normalization based method. In addition, a real data example about successive rises and falls of Shanghai stock exchange composite index yield is used to illustrate the proposed methodology.