in reply to
Estimating continuous functions
This sounds perfect for Bayesian networks.
While it is fairly easy to find implimentations of Beyesian Networks most are discrete not continuous like you want.
As hossman said "..that for any sets of points, there are an infinte number of curves that fit them, and except in simple cases, there's usually no way to determine that one curve is "more correct" then another..."
With Bayesian dependence modeling you can compare the probabilities of two models. if you know the probability of your data you could get the actual probability of the model.
One of the best places for reading more is the B-Course library at http://b-course.hiit.fi/library.html