Reversible Jump Markov Chain Monte Carlo: Some Theory and Applications

Abstract

The history of MCMC, theories of Bayesian thinking and model choice, the Accept- Reject-algorithm, Markov chains, the Metropolis- Hastings-algorithm and the reversible jump MCMC are explained. Then the reversible jump MCMC as change-point analysis is applied to the coal mine disaster example, familiar from [Green, 1995], and to the examples of counting terrorism attacks (worldwide, in Iraq and in Afghanistan). The novel part is estimating the change points of the hazard rate of terrorism attacks in Afghanistan during the last 35 years.