An overview of ordering defined on the space of Markov chains having a pre-specified distribution as their unique stationary distribution is provided. The intuition gained by studying these orderings is used to improve existing Markov chain Monte Carlo algorithms.

The class of finite state space Markov chains stationary with respect to a common pre-specified distribution is considered. An easy to check partial ordering is defined on this class. The ordering provides a sufficient condition for the dominating Markov chain to be more efficient. Efficiency is...

We propose a general purpose variance reduction technique for Markov Chain Monte Carlo estimators based on the Zero-Variance principle introduced in the physics literature by Assaraf and Caarel ( 1999). The potential of the new idea is illustrated with some toy examples and a real application to...

We exend Meng and Wong (1996) identity from a fixed to a varying dimentional setting. The identity is a very powerful tool to estimate ratios of normalizing constants and thus can be used to evaluate Bayes factors. The extention is driven by the reversibler jump algorithm so that the output from...

We propose a general purpose variance reduction technique for MCMC estimators. The idea is obtained by combining standard variance reduction principles known for regular Monte Carlo simulations (Ripley, 1987) and the Zero-Variance principle introduced in the physics literature (Assaraf and...

Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block...