Recent Advancements to Nonparametric Modeling of Interactions Between Reservoir Parameters

  • Håvard Goodwin Olsen
  • Gudmund Horn Hermansen
Part of the Quantitative Geology and Geostatistics book series (QGAG, volume 19)


We demonstrate recent advances in nonparametric density estimation and illustrate their potential in the petroleum industry. Here, traditional parametric models and standard kernel methodology may often prove too limited. This is especially the case for data possessing certain complex structures, such as pinch-outs, nonlinearity, and heteroscedasticity. In this paper, we will focus on the Cloud Transform (CT) with directional smoothing and Local Gaussian Density Estimator (LGDE). These are flexible nonparametric methods for density (and conditional distribution) estimation that are well suited for data types commonly encountered in reservoir modeling. Both methods are illustrated with real and synthetic data sets.


Kernel Density Kernel Density Estimation Kernel Smoothing Kernel Density Estimator Standard Kernel 
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.



We thank Arne Skorstad at Emerson Process Management – Roxar AS for providing the real data case. We also thank Dag Tjøstheim and Håkon Otneim for an early draft of the LGDE papers and for providing R code.


  1. Cressie N (1993) Statistics for spatial sata. Wiley series in probability and mathematical statisticsGoogle Scholar
  2. Hermansen G, Kolbjørnsen O, Abrahamsen P (2016) Extensions and applications of the cloud transform with directional smoothing. Norwegian Computing CenterGoogle Scholar
  3. Kolbjørnsen O, Abrahamsen P (2005) Theory of the cloud transform for applications. SpringerGoogle Scholar
  4. Leuangthong O, Deutsch CV (2003) Stepwise conditional transformation for simulation of multiple variables. Int Assoc Math Geol 35:155–173CrossRefGoogle Scholar
  5. Otneim H, Tjøstheim D (2016a) The local Gaussian density estimatorfor multivariate data. Stat ComputGoogle Scholar
  6. Otneim H, Tjøstheim D (2016b) Non-parametric estimation of conditional densities. A new method. Chapter 3.3 in the PhD thesis of Håkon Otneim, Department of Mathematics, University of Bergen, NorwayGoogle Scholar
  7. Sain SA (1994) Adaptive kernel density estimation. PhD thesisGoogle Scholar
  8. Sammut C, Webb GI (2010) Encyclopedia of machine learning. In: Encyclopedia of machine learning. Springer US, pp 257–258Google Scholar
  9. Silverman B (1998) Density estimation for statistics and data analysis. Chapman & Hall/CRC, LondonGoogle Scholar
  10. Wand M, Jones MC (1993) Comparison of smoothing parameterizations in bivariate kernel density estimation. Am Stat Assoc 88:520–528CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Håvard Goodwin Olsen
    • 1
  • Gudmund Horn Hermansen
    • 1
  1. 1.Norwegian Computing CenterOsloNorway

Personalised recommendations