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Title: Kriging Performance Without Kriging Complexity
Abstract: Among methods for interpolating scattered data, the method of kriging is often considered special because it not only makes highly accurate predictions, but also provides credible confidence intervals around those predictions. Alternative interpolation methods, such as radial basis functions or inverse-distance-weighted interpolation, make predictions that are typically less accurate and come without confidence intervals. However, kriging's advantages come at the cost of high conceptual complexity. While it is possible to explain radial-basis-function interpolation in one phrase – find a weighted combination of smooth basis functions that interpolates the data – explaining kriging in an intuitive manner is difficult. Simple short explanations such as "kriging models the unknown function as a realization of a stochastic process," while accurate, convey very little intuition to the typical engineer.
In this seminar, I show how to extend radial-basis-function methodology to improve its accuracy and provide confidence intervals without sacrificing the method's conceptual simplicity. Because the extended radial-basis-function methodology gives formulas for the predictor and confidence intervals that are essentially the same as those from kriging, it provides another way to understand these formulas, one that is more accessible to the typical engineer and may provide additional insights for the professional statistician.