5:21 PM
@user777 this is where I thought this was may be a novel idea
@user777 I may be completely wrong because I am just thinking out loud here as well
but my thought was that you still don't know what the analytical form of f(x) is and you don't actually have derivative observations from f'(x) either
my thought was can we write down the posterior predictive distribution of f'(x)|f(x)?
so can we predict what we think the derivative should look like based on the fact that we have observations of f(x)
clearly you could build a finite difference approximation to the derivative using the posterior predictive of f(x) (I have done this and it works beautifully)
@user777 but I think a more concrete solution, from a probabilistic or statistical point of view, would be better sought without an approximation