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Mathematical Geosciences

, Volume 46, Issue 3, pp 337–359 | Cite as

Projection Pursuit Multivariate Transform

  • Ryan M. Barnett
  • John G. Manchuk
  • Clayton V. Deutsch
Article

Abstract

Transforming complex multivariate geological data to a Gaussian distribution is an important and challenging problem in geostatistics. A variety of transforms are available for this goal, but struggle with high dimensional data sets. Projection pursuit density estimation (PPDE) is a well-established nonparametric method for estimating the joint density of multivariate data. A central component of the PPDE algorithm transforms the original data toward a multivariate Gaussian distribution. The PPDE approach is modified to map complex data to a multivariate Gaussian distribution within a geostatistical modeling context. Traditional modeling may then take place on the transformed Gaussian data, with a back-transform used to return simulated variables to their original units. This approach is referred to as the projection pursuit multivariate transform (PPMT). The PPMT shows the potential to be an effective means for modeling high dimensional and complex geologic data. The PPMT algorithm is developed before discussing considerations and limitations. A case study compares modeling results against more common techniques to demonstrate the value and place of the PPMT within geostatistics.

Keywords

Kernel Density Estimation Projection Pursuit Geostatistical Modeling Radial Point Interpolation Method Projection Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Ryan M. Barnett
    • 1
  • John G. Manchuk
    • 1
  • Clayton V. Deutsch
    • 1
  1. 1.Centre for Computational Geostatistics, Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada

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