Bayesian Radial Basis Function Interpolation

John Skilling and Sibusiso Sibisi
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John Skilling: University of Cambridge, Department of Applied Mathematics and Theoretical Physics
Sibusiso Sibisi: University of Cambridge, Department of Applied Mathematics and Theoretical Physics

A chapter in Computing Science and Statistics, 1992, pp 17-26 from Springer

Abstract: Abstract Interpolation using radial basis functions in one or more dimensions has become a subject of much research (e.g. Buhmann and Powell [1], Foley [2]). It is an example of inference problems involving incomplete and/or noisy data. All such inference problems ought to be analysed with ordinary (Bayesian) probability calculus, which is the only method of consistent inference (Cox [3]). Using Bayes’ theorem alone, with no extraneous devices, we are able to compute a probability distribution over the solution space for any given data. This approach allows the quantification of error bars or inference regions on the solution. The subject of inference regions in the context of Bayesian spline approximation is discussed by Wahba [4] and Silverman [5]. But the probabilistic formulation goes beyond this: for a given dataset, it provides a criterion for determining the best choice of radial basis function and its associated free parameters.

Keywords: Radial Basis Function; Inference Problem; Smooth Data; Inference Region; Spatial Correlation Structure (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-1-4612-2856-1_2

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