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Function Space Metropolis-Hastings Algorithms with Non-Gaussian Priors

Tuesday, February 11, 2020 - 1:25pm - 2:25pm
Lind 305
Bamdad Hosseini (California Institute of Technology)
Metropolis-Hastings (MH) algorithms are one of the most widely used methods for inference.
However, the convergence properties of these algorithms often deteriorate in high-dimensions
making them unsuitable for Bayesian inverse problems and non-parametric inference where,
in principle, the problem is defined on an infinite-dimensional Hilbert or Banach space.

In this talk we discuss some ideas for designing new MH algorithms that are reversible with
dimension-independent convergence properties. We present a new class of algorithms called
RCAR, that is tailored to priors based on the gamma distribution. We present an application of
RCAR for a deconvolution inverse problem and consider its convergence properties and consistent
approximation.

I am a von Karman instructor in the Department of Computing and Mathematical Sciences at California Institute of Technology, sponsored by Prof. Andrew Stuart. Prior to that I received my Ph.D. in Applied and Computational Mathematics in the Department of Mathematics at Simon Fraser University with of Profs. Nilima Nigam and John Stockie. I work on problems at the interface of probability, statistics and applied mathematics with a particular focus on the analysis, development and application of computational methods for estimating parameters and quantifying uncertainty.