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Infinite-dimensional Bayesian Inverse Problems: Theory, Computation and Applications
Date: 2016/12/6             Browse: 575
Seminar Topic:  Infinite-dimensional Bayesian Inverse Problems: Theory, Computation and Applications

Speaker: Jinglai Li
Time: Dec. 6, 10:00 a.m. - 11:00 a.m.
Venue:  Room 1B-106, SIST Building

Bayesian inference has become increasingly popular as a tool to solve inverse problems, largely due to its ability to quantify the uncertainty in the solutions obtained. In many practical problems such as image reconstructions, the unknowns are often of infinite dimension, i.e., functions of space and/or time. Theories and methods developed for finite dimensional problems may become problematic in the infinite dimensional setting and thus new theories and methods must be developed for such problems. In this talk we shall discuss several critical issues associated with the infinite dimensional problems and some efforts made to address them. First we discuss the Maximum a Posterior (MAP) estimation in this setting and its numerical implementations. Next we introduce a non-Gaussian prior for modeling functions that are subject to sharp jumps. We then present an efficient adaptive MCMC algorithm that is specifically designed for function space inference. Finally, we apply the Bayesian inference methods to a medical image reconstruction problem.

2012 : Distinguished Research Fellow, Shanghai Jiao Tong University
2010 - 2012: Research Associate, MIT
2007 - 2010: Research Associate, Northwestern University
Ph.D.,2007,The State University of New York at Buffalo

Research Interests:Scientific Computing, Computational Statistics, Uncertainty Quantification.

Seminar 16081