Publication Date

Summer 7-13-2021

Abstract

This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say from a seismic event. The Wasserstein metric can be generalized to multidimensional signals, but implementation of the multidimensional Wasserstein metric is very computationally expensive. This means that it is unreasonable for Bayesian inversion. Debiased Sinkhorn Divergence offers an alternative to the multidimensional Wasserstein metric while remaining relatively cheap computationally. This allows for the creation of a Debiased Sinkhorn Divergence driven Bayesian framework that will be formulated and analyzed in this paper.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Mohammad Motamed

Second Committee Member

Daniel Appelö

Third Committee Member

Gabriel Huerta

Fourth Committee Member

Stephen Lau

Language

English

Keywords

Bayes, Bayesian, Inversion, Signal Processing, Optimal Transport, Bayesian Inversion

Document Type

Thesis

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