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Bayesian Radial Basis Function Interpolation

In: Computing Science and Statistics

Author

Listed:
  • John Skilling

    (University of Cambridge, Department of Applied Mathematics and Theoretical Physics)

  • Sibusiso Sibisi

    (University of Cambridge, Department of Applied Mathematics and Theoretical Physics)

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.

Suggested Citation

  • John Skilling & Sibusiso Sibisi, 1992. "Bayesian Radial Basis Function Interpolation," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 17-26, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_2
    DOI: 10.1007/978-1-4612-2856-1_2
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