For half a century computational scientists have been numerically simulating complex systems. Uncertainty is recently becoming a requisite consideration in complex applications which have been classically treated deterministically. This has led to an increasing interest in recent years in uncertainty quantification (UQ). Another recent trend is the explosion of available data. Bayesian inference provides a principled and well-defined approach to the integration of data into an a priori known distribution. The posterior distribution, however, is known only point-wise (possibly with an intractable likelihood) and up to a normalizing constant. Monte Carlo methods have been designed to sample such distributions, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) samplers. Recently, the multilevel Monte Carlo (MLMC) framework has been extended to some of these cases, so that approximation error can be optimally balanced with statistical sampling error, and ultimately the Bayesian inverse problem can be solved for the same asymptotic cost as solving the deterministic forward problem. This talk will concern the recent development of ​various MLMC algorithms for Bayesian inference problems. This class of algorithms are expected to become prevalent in the age of increasingly parallel emerging ​computer ​architecture ​s​, where resilience and reduced data movement will be crucial algorithmic considerations. ​  These​​  methods are prototypical of a general trend of convergence between statistics and mathematics in computational science.  Some thoughts on the future of these subjects in connection to the new paradigm of data-intensive science ​ will also be discussed.
 
Speaker Biography:
Kody Law is a senior research mathematician in the Computer Science and Mathematics Division at Oak Ridge National Laboratory and joint Associate Professor at the University of Tennessee, Knoxville. He received his PhD in Mathematics from the University of Massachusetts in 2010, and subsequently held positions at the University of Warwick and King Abdullah University of Science and Technology before joining ORNL in 2015.  He has published in the areas of computational applied mathematics, probability, statistics, physics, and dynamical systems. His current research interests are focused on inverse uncertainty quantification: data assimilation, filtering, and Bayesian inverse problems.