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merliseclyde / sta701-F23

STA 701S Fall 2023
https://merliseclyde.github.io/sta701-F23/
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Title & Abstract #28

Closed ybaek closed 8 months ago

ybaek commented 8 months ago

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title: "Generalized Bayes Approach to Inverse Problems with Model Misspecification"

author: "Youngsoo Baek"

date: "Nov 20, 2023"

Abstract

I discuss a general framework for obtaining probabilistic solutions to PDE-based inverse problems when potentially the PDE is inaccurate or the noise-generating mechanism is unknown. In a generalized Bayesian formulation, the Bayesian update problem is reformulated and generalized into a regularized variational problem on the space of probability distributions of the parameter. A novel generalization of a Bayesian model comparison procedure is given for evaluating the optimality of a given loss based on its "predictive performance." A tailored sequential Monte Carlo-based approach is used to simultaneously calibrate the regularization parameter and obtain samples from the underlying posterior. Some theoretical properties of Gibbs posteriors are also presented.

Advisor(s)

Sayan Mukherjee

merliseclyde commented 8 months ago

Thanks - shoujld appear on the website shortly