## Advances in Markov chain (2007)

### BibTeX

@MISC{Methods07advancesin,

author = {Monte Carlo Methods and Iain Murray},

title = {Advances in Markov chain},

year = {2007}

}

### OpenURL

### Abstract

I, Iain Murray, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 3 Probability distributions over many variables occur frequently in Bayesian inference, statistical physics and simulation studies. Samples from distributions give insight into their typical behavior and can allow approximation of any quantity of interest, such as expectations or normalizing constants. Markov chain Monte Carlo (MCMC), introduced by Metropolis et al. (1953), allows sampling from distributions with intractable normalization, and remains one of most important tools for approximate computation with probability distributions. While not needed by MCMC, normalizers are key quantities: in Bayesian statistics marginal likelihoods are needed for model comparison; in statistical physics many physical quantities relate to the partition function. In this thesis we propose and investigate several new Monte Carlo algorithms, both for evaluating normalizing constants and for