# Reversible Jump Markov Chain Monte Carlo Methods

## Introduction

This web page contains supplementary material for the following
project:

- Ai Jialin, Reversible Jump Markov Chain Monte Carlo Methods.

MSc thesis, University of Leeds, Department of Statistics, 2011/12.

## Abstract

This dissertation is about the reversible-jump Markov chain Monte
Carlo (RJMCMC) method in Bayesian statistics and its application to
solving the change-points problem. A change-points problem is to
determine the parameters of a step model with ﬂexible number of
steps. This model is widely used in different ﬁelds. Thus many
application, such as change-points in genes determining and ﬂexible
number’s variables selection in regression, beneﬁt from RJMCMC.

Firstly I introduce Markov chain Monte Carlo (MCMC) and the
Metropolis-Hastings (MH) Algorithm. I explain the concept
“reversibility”, give the relationship between “reversible” and
“stationary”, and then prove that the Markov chain generated by M-H is
reversible and stationary.

Secondly, I introduce Bayesian estimation and realise it with M-H
algorithm. I gave a simple and clear example and implement it in R
with Bayesian estimates algorithm. Next, I introduced the subspaces
assumption of reversible-jump Markov chain, and the basic form of the
acceptance probability jumping between subspaces of differing
dimensionality based on Green (1995).

Finally, I try to solve a change-points problem of coal-mining
disasters data. I calculate the acceptance probabilities of different
move types, combine the results and the Metropolis Hastings algorithm
into an R program. And I also analyse the reversible-jump Markov chain
generated by the program.

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