# Graduate Student / Postdoc Seminar

#### Simple ensemble strategies for preconditioning Markov chain Monte Carlo

**Speaker:**
Jonathan Weare, Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, February 8, 2019, 1 p.m.

**Synopsis:**

Markov chain Monte Carlo methods estimate averages with respect to a given probability density (e.g. a paremeter posterior density) by a generating a long trajectory of a Markov process with the right ergodic distribution and assembling the appropriate average over the trajectory. In many practical applications, maintaining stability (or a reasonable acceptance rate) requires using a Markov chain with very small increments. A similar problem arises in optimization, where efficient and practical preconditioning techniques (changes of variables that alleviate the restriction on perturbations) have been developed over many decades. Unfortunately, the most practical and widely used of these techniques do not have analogues in the sampling context. I'll describe a framework for preconditioning the underdamped Langevin sampling technique and suggest some very simple preconditioning strategies based on estimating local covariance information from parallel Markov chain Monte Carlo methods. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.