The use of systems of stochastic PDEs as priors for multivariate models with discrete structures

TL;DR

This paper introduces a novel method using systems of stochastic PDEs as priors for multivariate models with discrete structures, enabling flexible, computationally efficient modeling of complex geologic interfaces.

Contribution

It proposes a new parametrization of correlations across discrete structures and a geodesic blending technique to quantify interface fuzziness, enhancing prior modeling in multivariate problems.

Findings

Efficient sparse precision matrices for complex models

Flexible correlation parametrization across structures

Quantification of interface fuzziness using geodesic blending

Abstract

A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seismic amplitude versus angle (AVA) inversion to elastic parameters, where the discrete structures are geologic layers. Recently, the use of systems of linear stocastic partial differential equations (SPDEs) have become a popular tool for specifying priors in latent Gaussian models. This approach allows for flexible incorporation of nonstationarity and anisotropy in the prior model. Another advantage is that the prior field is Markovian and therefore the precision matrix is very sparse, introducing huge computational and memory benefits. We present a novel approach for parametrising correlations that differ in the different discrete structures, and additionally a geodesic blending approach for quantifying fuzziness of interfaces between the structures. Keywords: Gaussian distribution, multivariate, stochastic PDEs, discrete structures