2008 Volume 4 Issue 1 Pages 85-100
One of the purposes of this paper is achieving the automatic scale adjustment of the proposal distribution in the random-walk Metropolis-Hastings algorithm and the automatic convergence detection of Markov chains. In order to realize the purpose, the parallel Markov chain Monte Carlo algorithm based on the idea suggested by Gelman, Roberts & Gilks (1996) is proposed. The remarkable feature of the proposed algorithm is that effective samples can be obtained immediately after the scale adjustment of the proposal distribution and the convergence detection of Markov chains are completed simultaneously. Another purpose of this paper is to apply the proposed algorithm to the parameter estimation of the Rasch model which is one of the item response models. Simulation results show that the item difficulties of the Rasch model can be estimated properly by the parallel single-component random-walk Metropolis-Hastings algorithm.
