Full Bayesian approach to curve and surface reconstruction

When interpolating incomplete data, a parametric model can be chosen, or a more general approach can be considered and use a nonparametric model which allows a very large class of interpolants. A popular non-parametric model for interpolating various types of data is based on regularization, which looks for an interpolant that is both close to the data and also smooth in some sense. The classical approach to regularization is select optimal weights that should be assigned to these two terms, and minimize the resulting error functional. A method which uses full probability distribution on the space of admissable functions, as opposed to the probability induced by using a single combination of weights, is proposed.