Constructing space-time pdfs in Geosciences

Authors

  • G. Christakos Dept of Geography, SdSU - College of the Environment & Natural Resources, Zhejiang University
  • J. M. Angulo Dept of Statistics and Operations Research, UG
  • H.-L. Yu Dept of Bioenvironmental Systems Engineering, NTU

DOI:

https://doi.org/10.21701/bolgeomin.122.4.009

Keywords:

BME, copulas, factoras, multivariate, probability, spatiotemporal

Abstract


The focus of this work is the comparative analysis of techniques for constructing multivariate probability density function (Mv-pdf) models that can be used in a variety of geomathematics applications. The paper is concerned with formal and substantive model building methods. The former includes models that are speculative and analytically tractable, whereas the latter is based on substantive knowledge synthesis. More specifically, the present work focuses on the factoras and copulas techniques of Mv-pdf building, and their comparative analysis. It also discusses a substantive Mv-pdf building method that generates models on the basis of natural knowledge bases and takes into account the contentual and contextual domain of the in situ situation. The methods are compared in terms of a simulation study.

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References

Akita Y., Carter G., and Serre M. L. 2007. Spatiotemporal non-attainment assessment of surface water tetrachloroethene in New Jersey. Jour of Environmental Quality 36(2): 508-520. https://doi.org/10.2134/jeq2005.0426

Bardossy, A. and Li, J., 2008. Geostatistical interpolation using copulas. Water Resources Research 44(7): W07412. https://doi.org/10.1029/2007WR006115

Christakos G. 1986. Recursive estimation of nonlinear-state nonlinear-observation systems. Research Rep. OF.86-29, Kansas Geological Survey, Lawrence, KS.

Christakos G. 1989. Optimal estimation of nonlinear-state nonlinear-observation systems. Jour. of Optimization Theory and Application 62: 29-48. https://doi.org/10.1007/BF00939628

Christakos G. 1990. A Bayesian/maximum-entropy view to the spatial estimation problem. Mathematical Geology 22(7): 763-776. https://doi.org/10.1007/BF00890661

Christakos, G. 1992. Random Field Models in Earth Sciences. Academic Press, San Diego, CA.

Christakos, G. 2000. Modern Spatiotemporal Geostatistics. Oxford Univ. Press, New York, NY.

Christakos, G. 2010. Integrative Problem-Solving in a Time of Decadence. Springer, New York, NY. https://doi.org/10.1007/978-90-481-9890-0

de la Peña V.H., Ibragimov R. and Sharakhmetov S. 2006. Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series. IMS Lecture Notes-Monograph Series 2nd Lehmann Symposium-Optimality 49: 183-209. https://doi.org/10.1214/074921706000000455

Douaik A., van Meirvenne M., Toth T. and Serre M. L. 2004. Space-time mapping of soil salinity using probabilistic BME. Stochastic Environmental Research and Risk Assessment 18: 219-227. https://doi.org/10.1007/s00477-004-0177-5

Emery X. 2006. A disjunctive kriging program for assessing point-support conditional distributions. Computers & Geosciences 32(7): 965-983 https://doi.org/10.1016/j.cageo.2005.10.011

Genest C. and Nešlehová J. 2007. A primer on copulas for count data. Astin Bulletin 37(2): 475-515. https://doi.org/10.2143/AST.37.2.2024077

Genest C. and Rivest L.-P. 1993. Statistical inference procedures for bivariate Archimedean copulas. Jour. of American Statistical Association 88: 1034-1043. https://doi.org/10.1080/01621459.1993.10476372

Joe H. 2006. Discussion of 'Copulas: Tales and facts,' by Thomas Mikosch. Extremes 9: 37-41. https://doi.org/10.1007/s10687-006-0019-6

Kazianka H. and Pilz J. 2010a. Copula-based geostatistical modeling of continuous and discrete data including covariates. Stochastic Environmental Research and Risk Assessment 24(5): 661-673. https://doi.org/10.1007/s00477-009-0353-8

Kazianka H. and Pilz J. 2010b. Spatial interpolation using copula-based geostatistical models. In GeoEnv VII: Geostatistics for Environmental Applications: 307-319. Atkinson P.M.M. and Lloyd C.D.D. (eds), Springer, New York, NY. https://doi.org/10.1007/978-90-481-2322-3_27

Kotz S. and Seeger J.P. 1991. A new approach to dependence in multivariate distributions. In Advances in Probability Distributions: 113-127, Dall'Aglio G., Kotz S. and Salinetti G. (eds.), Kluwer, Dordrecht, the Netherlands. https://doi.org/10.1007/978-94-011-3466-8_6

Kotz S., Balakrishnana N., and Johnson N.L. 2000. Continuous Multivariate Distributions. Wiley, New York, NY. https://doi.org/10.1002/0471722065

Long D. and Krzysztofowicz R. 1995. A family of bivariate densities constructed from marginals. Jour of the Amer. Statist. Assoc. 90(430): 739-746. https://doi.org/10.1080/01621459.1995.10476567

Mikosch T. 2006a. Copulas: tales and facts. Extremes 9: 3-20. https://doi.org/10.1007/s10687-006-0015-x

Mikosch T. 2006b. Copulas: tales and facts-rejoinder. Extremes 9: 55-62. https://doi.org/10.1007/s10687-006-0024-9

Nelsen, R. 1999. An Introduction to Copulas. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3076-0

Olea R. A., 1999. Geostatistics for Engineers and Earth Scientists. Kluwer Acad. Publ., Boston, MA. https://doi.org/10.1007/978-1-4615-5001-3

Parkin R., Savelieva E., and Serre M. L. 2005. Soft geostatistical analysis of radioactive soil contamination. In GeoEnv V-Geostatistics for environmental applications. Renard Ph. (ed.). Kluwer Acad., Dordrecht, the Netherland.

Pearson K. 1901. Mathematical contributions to the theory of evolution, VII: On the correlation of characters not quantitatively measurable: Philosophical Trans. Royal Soc. of London, Series A 195: 1-47. https://doi.org/10.1098/rsta.1900.0022

Savelieva E., Demyanov V., Kanevski M., Serre M. L., and Christakos G. 2005. BME-based uncertainty assessment of the Chernobyl fallout. Geoderma 128: 312-324. https://doi.org/10.1016/j.geoderma.2005.04.011

Scholzel, C., & Friederichs, P. (2008). Multivariate non-normally distributed random variables in climate research - introduction to the copula approach. Nonlinear Processes in Geophysics 15: 761-772. https://doi.org/10.5194/npg-15-761-2008

Serinaldi, F. 2008. Analysis of inter-gauge dependence by Kendall's tk, upper tail dependence coefficient, and 2-copulas with application to rainfall fields. Stochastic Environmental Research and Risk Assessment 22(6): 671-688. https://doi.org/10.1007/s00477-007-0176-4

Serinaldi, F. 2009. Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective. Stochastic Environmental Research and Risk Assessment 23(5): 677-693. https://doi.org/10.1007/s00477-008-0249-z

Sklar A. 1959. Fonctions de repartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de L'Universite de Paris 8: 229-231, Paris, France.

Song S. and Singh V.P. 2010a. Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stochastic Environmental Research and Risk Assessment 24(3): 425-444. https://doi.org/10.1007/s00477-009-0331-1

Song S. and Singh V.P. 2010b. Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stochastic Environmental Research and Risk Assessment 24(5): 783-805. https://doi.org/10.1007/s00477-010-0364-5

Sungur E.A. 1990. Dependence information in parameterized copulas. Commun. Statist.-Simula. 19(4): 1339-1360. https://doi.org/10.1080/03610919008812920

Shvidler M. I. 1965. Sorption in a plane-radial filtration flow. Journal of Applied Mechanics and Technical Physics 6(3): 77-79. https://doi.org/10.1007/BF00913438

Vyas V. M., Tong S. N., Uchrin C., Georgopoulos P. G., and Carter G. P. 2004. Geostatistical estimation of horizontal hydraulic conductivity for the Kirkwood-Cohansey aquifer. Jour of the American Water Resources Associates 40(1): 187-195. https://doi.org/10.1111/j.1752-1688.2004.tb01018.x

Yu H.-L., Christakos G., Modis K., and Papantonopoulos G. 2007a. A composite solution method for physical equations and its application in the Nea Kessani geothermal field (Greece). Jour of Geophysical Research-Solid Earth 112: B06104. https://doi.org/10.1029/2006JB004900

Yu H.-L., Kolovos A., Christakos G., Chen J.-C., Warmerdam S., and Dev B. 2007b. Interactive spatiotemporal modelling of health systems: the SEKS-GUI framework. Stochastic Environmental Research and Risk Assessment 21(5): 555-572. https://doi.org/10.1007/s00477-007-0135-0

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Published

2011-12-30

How to Cite

Christakos, G., Angulo, J. M., & Yu, H.-L. (2011). Constructing space-time pdfs in Geosciences. Boletín Geológico Y Minero, 122(4), 531–542. https://doi.org/10.21701/bolgeomin.122.4.009

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