Abstract
Procedures using splines for estimating values of linear functionals of an unknown function based on finitely many possibly noisy observations of function values are reviewed taking a Bayesian point of view. Interpolation with splines is emphasized as an example of Bayesian numerical analysis, smoothing with splines is presented as interpolation in estimated function values. Extensions of the approach to estimating values of non-linear functionals applied to the unknown function and to estimation subject to linear constaints on the unknown function are discussed. Furthermore, invariance of Bayesian inference to modifications of the prior distribution, resulting from alternative choices of an appropriate function space for estimation, is addressed, too.
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