Statistics Seminar: Pierre E. Jacob
Speaker: Pierre E. Jacob
Title: Couplings of Markov chains and the Poisson equation
Abstract: Many statistical adventures involve the task of sampling from probability distributions. In general, this task requires non-trivial computational methods. Markov chain Monte Carlo methods constitute a wide and popular class of algorithms that iteratively construct a sequence of random variables, with the guarantee that the distribution of interest is attained in the limit of the number of iterations. This talk will describe some old and new tools, based on couplings and the Poisson equation, to decide on the number of iterations to perform, taking bias and variance into account. Illustrations include a "donkey walk" related to Dempster-Shafer inference, a simple Markov chain to sample from conditional Bernoulli distributions, and Gibbs samplers for high-dimensional regression with shrinkage priors.
Bio: Dr. Pierre E. Jacob is a tenure-track faculty in the Department of Statistics at Harvard University. He received a PhD from Université Paris Dauphine in France in 2012, then worked as a postdoc at the National University of Singapore and the University of Oxford before moving to the US in 2015. He develops methods of statistical inference and Monte Carlo algorithms, with a focus on particle filters, Markov chains and probability couplings. His research is partially supported by a National Science Foundation CAREER award, and he received the 2021 Guy Medal in Bronze from the Royal Statistical Society.
All School of Statistics Seminars are open to the public. A virtual social will take place from 10:30-11:30AM CDT, following this seminar. To join, visit here.
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