Abstract: According to the cumulative number of shopping people in a mall, we established the poisson process model with periodic single change point, and studied the full conditional distributions of period and other parameters. Under the conditions of absolute loss and squared loss as the loss function, we discussed the Bayesian estimation of unknown parameters by using Gibbs and MetropolisHastings algorithms. The results of random simulation and example analysis show that Bayesian estimations of two kinds of loss functions have good accuracy.

Key words: MCMC (Markov chain Monte Carlo) method, MetropolisHastings algorithm, Bayesian estimation, Gibbs sampling