Improving the efficiency of Markov chain Monte Carlo

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Markov chain Monte Carlo (MCMC) algorithms are widely used in the scientific community. They are used to generate approximate samples from complicated target distributions resulting from statistical and applied probability models. In particular, generic algorithms such as Metropolis and Langevin algorithms are very popular because of the ease of implementations. However, it is well known that choosing the best proposal distribution is not an easy task. Failing to do that can result in an inefficient algorithm and misleading results. My research program will focus on the theory and implementation of MCMC algorithms, typically on unbounded Euclidean state spaces, motivated by distributions such as those encountered in Bayesian inference. The three main objectives of my proposed research program are: