We use the Bayesian bootstrap clones procedure developed by Lo (1991) to simulate the posterior distributions of the transition probabilities, the stationary probabilities and the cdf of the first hitting time of a specific state for a finite state ergodic Markov chain. The large sample theory shows that, with a conjugate prior on the transition probability, both the posterior distribution and the Bayesian bootstrap clones procedure are first-order consistent, but the second order of the Bayesian bootstrap clones depends on the skewness of the random variables generated in the procedure. Small sample cases of the Bayesian bootstrap clones are also studied by simulation.
