pigeons in holes

The loyal reader knows that Dan Foreman-Mackey and I are working on building toy problems for inference (that is, priors and likelihood functions) that contain nasty but realistic degeneracies for testing MCMC and fully marginalized likelihood (FML) computations. I got the first version of the code working today, and performed some minimal unit tests.

The code builds a mixture of M-choose-K times K-factorial Gaussians in KD-dimensional space such that the model has all combinatoric degeneracies from (a) not knowing which of the M holes to put the K pigeons into and (b) not knowing which pigeon is which (labeling degeneracy). This mixture of Gaussians gets huge fast, but as long as the prior is also a mixture of Gaussians, perfect sampling, exact marginalization, and analytic FML calculations are all possible without MCMC; it is therefore a perfect testbed.

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