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Projection Pursuit Multivariate Transform

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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.

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Authors and Affiliations

  1. Centre for Computational Geostatistics, Department of Civil and Environmental Engineering, University of Alberta, 3-133 NREF Building, Edmonton, Alberta, T6G 2W2, Canada

    Ryan M. Barnett, John G. Manchuk & Clayton V. Deutsch

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  1. Ryan M. Barnett
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  2. John G. Manchuk
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  3. Clayton V. Deutsch
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Correspondence to Ryan M. Barnett.

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Barnett, R.M., Manchuk, J.G. & Deutsch, C.V. Projection Pursuit Multivariate Transform. Math Geosci 46, 337–359 (2014). https://doi.org/10.1007/s11004-013-9497-7

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  • DOI: https://doi.org/10.1007/s11004-013-9497-7

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