I am working with a deconvolution model in which the convolved distribution of probability is obtained via deconvolved distribution as:

f_Y(y)=\int_{y}^{\infty}A(x,y,\theta)f_X(x).

Where A(x,y,\theta) is the response known function (or response matrix if we discretize data) and \theta is a parámeter of the function. My question is: can i obtain f_X(x) and \theta as a parameters vector from and observed vector y_i doing HMC in Stan?

I was thinking to think f_X(x) as a vector of parameters that can be estimated doing HMC with \theta as well. There is an advice to model this integral representation in STAN?

Hi,
I don’t think I understand your model very well. Is f_X known? Is x known? In any case, the general rule is that:

If you have a deterministic algorithm that can compute the density of y given \theta, you can almost always express that in Stan (e.g. there is support for integration as a part of a Stan program: 14 Computing One Dimensional Integrals | Stan User’s Guide)

If you can write a simulator that generates data according to your model, you can very often translate it into an algorithm that copmputes the density (and that can be expressed in Stan)