A map-based approach to Bayesian inference in inverse problems

Wednesday, June 8, 2011 - 2:30pm - 3:30pm
Keller 3-180
Youssef Marzouk (Massachusetts Institute of Technology)
Bayesian inference provides a natural framework for quantifying
uncertainty in PDE-constrained inverse problems, for fusing
heterogeneous sources of information, and for conditioning successive
predictions on data. In this setting, simulating from the posterior
via Markov chain Monte Carlo (MCMC) constitutes a fundamental
computational bottleneck. We present a new technique that entirely
avoids Markov chain-based simulation, by constructing a map under
which the posterior becomes the pushforward measure of the
prior. Existence and uniqueness of a suitable map is established by
casting our algorithm in the context of optimal transport theory. The
proposed maps are analytically and efficiently computed using
various optimization methods.
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