I am modeling a large number of Dose-response curves. I have strong reason to believe that the generating function will be sigmoidal against the concentration of the assay (Michaelis-Menten kinetics). I also know that there will be no effect at 0 concentration (homeopathy is not real). I have been playing with using Gaussian Process regression because I really like the idea of being able to model my uncertainty and sometimes I only have noisy measurements at a couple of concentrations over a given curve.
Is there a Gaussian Process Kernel that limits functions to sigmoids? There is no example in Duvenaud's excellent kernel cookbook.
I have seen people mention such a thing, but I cannot find any concrete expression of such a kernel. Also, I cannot think of a way to use a covariance matrix to express ideas like monotonicity or sigmoidalness, maybe I have a fundamental confusion about GPs