Venturecxx
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probcomp
Do we want make_gamma_crp?
According to http://web.cse.ohio-state.edu/~kulis/teaching/788_sp12/DP.learnalpha.pdf, the gamma distribution is a conjugate (*) prior for the alpha parameter of a Chinese Restaurant Process. Do we want to capture this observation in a collapsed or uncollapsed procedure?
(*) The posterior is apparently a mixture of gammas rather than a single gamma, so this is not exactly the same functional form, but is nonetheless analytic.
I think it is a good idea, with relatively little effort we can characterize the sensitivity of CRP to the prior on alpha (in terms of mixing time/accuracy), which is not a study I have seen anyone actually do.
Taking a closer look at that paper, it looks like the thing described is not actually an exact posterior sampler, but an auxiliary variable Gibbs sampler -- p(alpha|k) is the marginal of a p(alpha,x|k), in which p(x|alpha,k) and p(alpha|x,k) are familiar distributions (beta and mixture-of-gamma, respectively).
So this is actually not necessarily much better than slice sampling for alpha, which is a procedure that samples p(u|alpha,k) and p(alpha|u,k). (This method is probably cheaper than slice sampling, and might mix better, but they don't provide evidence for that.)
Would be an example of an SP with a nontrivial latent that wasn't a perfect conjugate model, then. That almost makes me want to do it more, to include that kind of object in our vocabulary.
Project management decision: Do we want to do this to force ourselves to confront the kind of beast that this SP is? May also need understanding the paper and/or planning for how to add this kind of object, if it does turn out to be meaningfully different.