Semivariogram Methods for Modeling Whittle-Matérn Priors in Bayesian Inverse Problems

Document Type

Presentation Abstract

Presentation Date

11-4-2019

Abstract

In this talk, I will briefly present a mathematical description of the connection between Gaussian processes with covariance operators defined by the Matérn covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs) in the isotropic case. I will show that this connection breaks down when the domain is finite due to the effect of boundary conditions and that it can be re-established using extended domains. I will then introduce the semivariogram method for obtaining point estimates of the Whittle-Matérn covariance parameters, which completely specifies the Gaussian prior needed for stabilizing the inverse problem. I will extend these results to the anisotropic case, where the correlation length in one direction is larger than another. Finally, I will consider the case where the the correction length is spatially dependent. Two-dimensional image examples will be presented throughout the talk.

Additional Details

Monday, November 4, 2019 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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