How can I add observation in input and output : Yobs=f(X,Xobs)

(I hope I am not asking a question that has already been asked)

In the documentation or examples, I could learn to solve the following problem:
For Y=f(X1,X2), with the observations Y it is possible to determine the distributions of X1 and X2

In my case, I have Y=f(X1,X2,P) and with the observations of Y and P I would like to identify the distributions of X1 and X2. (The size of P is equal to 1e4)

Could you tell me how to include the P observations as input to my f model?

Thanks !