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Statistica Sinica 7(1997), 1005-1019



Cheng-Der Fuh and Tsai-Hung Fan

Academia Sinica and National Central University

Abstract: The Bayesian bootstrap for Markov chains is the Bayesian analogue of the bootstrap method for Markov chains. We construct a random-weighted empirical distribution, based on i.i.d. exponential random variables, to simulate the posterior distribution of the transition probability, the stationary probability, as well as the first hitting time up to a specific state, of a finite state ergodic Markov chain. The large sample theory is developed which shows that with a matrix beta prior on the transition probability, the Bayesian bootstrap procedure is second-order consistent for approximating the pivot of the posterior distributions of the transition probability. The small sample properties of the Bayesian bootstrap are also discussed by a simulation study.

Key words and phrases: Bayesian bootstrap, hitting time, Markov chain, matrix beta distribution, transition probability.

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