Building on crossvalidation for increasing the quality of geostatistical modeling |
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Authors: | Ricardo A Olea |
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Institution: | (1) U.S. Geological Survey, 12201 Sunrise Valley Dr., MS 956, Reston, VA 20192, USA |
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Abstract: | The random function is a mathematical model commonly used in the assessment of uncertainty associated with a spatially correlated
attribute that has been partially sampled. There are multiple algorithms for modeling such random functions, all sharing the
requirement of specifying various parameters that have critical influence on the results. The importance of finding ways to
compare the methods and setting parameters to obtain results that better model uncertainty has increased as these algorithms
have grown in number and complexity. Crossvalidation has been used in spatial statistics, mostly in kriging, for the analysis
of mean square errors. An appeal of this approach is its ability to work with the same empirical sample available for running
the algorithms. This paper goes beyond checking estimates by formulating a function sensitive to conditional bias. Under ideal
conditions, such function turns into a straight line, which can be used as a reference for preparing measures of performance.
Applied to kriging, deviations from the ideal line provide sensitivity to the semivariogram lacking in crossvalidation of
kriging errors and are more sensitive to conditional bias than analyses of errors. In terms of stochastic simulation, in addition
to finding better parameters, the deviations allow comparison of the realizations resulting from the applications of different
methods. Examples show improvements of about 30% in the deviations and approximately 10% in the square root of mean square
errors between reasonable starting modelling and the solutions according to the new criteria. |
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