Title

A truly multivariate normal score transform based on lagrangian flow

Document Type

Book Chapter

Publisher

Springer

Place of Publication

Cham, Switzerland

School

School of Science

RAS ID

26251

Comments

Originally published as: Mueller U., van den Boogaart K.G., Tolosana-Delgado R. (2017) A Truly Multivariate Normal Score Transform Based on Lagrangian Flow. In: Gómez-Hernández J., Rodrigo-Ilarri J., Rodrigo-Clavero M., Cassiraga E., Vargas-Guzmán J. (eds) Geostatistics Valencia 2016. Quantitative Geology and Geostatistics, vol 19. Springer, Cham. Original article available here

Abstract

In many geostatistical applications, a transformation to standard normality is a first step in order to apply standard algorithms in two-point geostatistics. However, in the case of a set of collocated variables, marginal normality of each variable does not imply multivariate normality of the set, and a joint transformation is required. In addition, current methods are not affine equivariant, as should be required for multivariate regionalized data sets without a unique, canonical representation (e.g., vector-valued random fields, compositional random fields, layer cake models). This contribution presents an affine equivariant method of Gaussian anamorphosis based on a flow deformation of the joint sample space of the variables. The method numerically solves the differential equation of a continuous flow deformation that would transform a kernel density estimate of the actual multivariate density of the data into a standard multivariate normal distribution. Properties of the flow anamorphosis are discussed for a synthetic application, and the implementation is illustrated via two data sets derived from Western Australian mining contexts.

DOI

10.1007/978-3-319-46819-8_7

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