Speeding up Metropolis Using Theorems

Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis algorithm, are designed to converge to complicated high-dimensional target distributions, to facilitate sampling. The speed of this convergence is essential for practical use. In this talk, we will present several theoretical results which can help improve the Metropolis algorithm’s convergence speed. Specific topics will include: diffusion limits, optimal scaling, optimal proposal shape tempering, adaptive MCMC, the Containment property, and the notion of adversarial Markov chains. The ideas will be illustrated using the simple graphical example available at probability.ca/met. No particular background knowledge will be assumed.

About Jeffrey Rosenthal

Jeffrey Rosenthal is a professor of Statistics at the University of Toronto, specialising in Probability theory, Markov chain Monte Carlo (MCMC) algorithms, and interdisciplinary applications of Statistics. He received his BSc from the University of Toronto in 1988, and his PhD in Mathematics from Harvard University in 1992. He was awarded the 2006 CRM-SSC Prize, the 2007 COPSS Presidents’ Award, the 2013 SSC Gold Medal, fellowship of the Institute of Mathematical Statistics and of the Royal Society of Canada, and teaching awards at both Harvard (1991) and Toronto (1998). He has published over 150 research papers, and five books, including the bestseller Struck by Lightning: The Curious World of Probabilities. He also does frequent media interviews and public lectures. His web site is probability.ca.