# Deconvolution in Stan

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)

Best of luck with your model!

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