I would like to ask for advice on choosing a suitable modelling method for the following problem:
I am modeling the performance of a device for curve estimation. I have collected a data set consisting of $3^{rd}$ degree polynomial curves (red), where the true $3^{rd}$ degree polynomial curve is in bold green. I need to model the true curve with uncertainty at each point, like shown on the second part of the figure*.
Note, that the resulting model has increasing variance as the curve estimation is less accurate the further away from the device the data is acquired.
*Please excuse the comically crude drawing
I have some machine learning background, so my best (and only) guess would be to use a Gaussian Process regression, which seems suitable since it results in a model with included uncertainty. However, the data I have seems more like samples from the posterior of the GP, and not data over which I could do regression.
So, I am hoping to hear your opinions on which modelling methods are most suitable and why.