A Methodological Study of the Application of the Maximum Entropy Estimator to Spatial Interpolation
Journal of Geographic Information and Decision Analysis, Vol. 2., No. 2, pp. 243-251, 1998.
This study applies the maximum entropy estimator to the interpolation of daily rainfall measurements in Switzerland taken on April 26, 1986. The major purpose of the paper is to introduce the methodology of maximum-entropy spatial interpolation. The accuracy of the estimation measured by the coefficient of determination is therefore only at the value of 0.0114. Moreover, the estimation errors are, to some extent, correlated to the real measurements. The larger the measurement is, the more severe the error becomes. The structure analysis on the 100 measurements used for estimation depicts the properties of anisotropy and non-stationarity in spite of the assumptions of second-order stationarity and isotropic correlation. The estimation errors, however, seem to be spatially independent. The spatial correlation coefficients of the errors (calculated based on the construction of the correlogram of the estimation errors) are only at the order of 0.01.
Keywords: Shannon?s Entropy, Maximum Entropy Principle, Lognormal Random Field, Simple Kriging, Log-Kriging.