I would like to implement a DPM model in Stan. My idea was to use the generalized Polya urn algorithm, but in order to do so I need to be able to sample from a mixture of a continuous distribution and a dirac delta. The problem is how to deal with the delta in Stan.
My idea is to approximate it with a normal distribution centred in the support of the delta and with an almost zero variance. How bad is this idea? I am not expert of HMC/MCMC algorithms and I can’t imagine what sampling problems could create this approximation.
Have you any better solution to this problem?
I know that one could implement DPM via stick-breaking (truncated) construction, in this way I can just see the weights and the center of each mixture component, but can’t do clusters analysis! (right?)