Speaker:  Jan Glaubitz (MIT)

Title:  Sparsity-promoting hierarchical Bayesian learning for inverse problems

Abstract:

Recovering sparse generative models from limited and noisy measurements presents a significant and complex challenge. Given that the available data is frequently inadequate and affected by noise, assessing the resulting uncertainty in the relevant parameters is crucial. Notably, this parameter uncertainty directly impacts the reliability of predictions and decision-making processes.

In this talk, we explore the sparsity-promoting hierarchical Bayesian learning framework, which facilitates the quantification of uncertainty in parameter estimates by treating involved quantities as random variables and leveraging the posterior distribution. 

Within the Bayesian framework, sparsity promotion and computational efficiency can be attained with hierarchical models with conditionally Gaussian priors and gamma hyper-priors.

Parts of this talk are joint work with Anne Gelb (Dartmouth) and Youssef Marzouk (MIT).

Keywords: hierarchical Bayesian Inverse problems, hierarchical Bayesian learning, sparsity, uncertainty quantification.