Consider a model with a prior p(\theta) = \alpha \delta(\theta) + (1-\alpha), \theta\in[0,1], where \alpha is a known parameter and \delta is Dirac’s delta, and possibly other unknown parameters as well. The particular form of the likelihood doesn’t matter much here I think.
The goal is to be able to compute expectations w.r.t. the posterior \theta|D.
Are there any tricks to encode this in Stan, or to encode only the continuous part and then somehow combine with the discrete part outside of Stan? All I can come up with requires calculating the total evidence p(D).