As seemingly anticipated by my discussion of the Dirichlet Process in my weak convergence talk at Imperial (see previous post)—in which I highlighted the potential of the DP for astronomical model analyses—today on astro ph we have an application of the DP (as infinite mixture of Normals) for modelling properties of the galaxy distribution in the context of weak lensing by Schneider et al. Now if someone could go ahead and code up the DP infinite mixture model as a replacement for the EM step in Kelly (2007), add GLM regression likelihoods, and release this as a package that would be great.

The only quibble I have with the Schneider et al. paper, by the way, is that again (see three posts ago) they use the importance sampling approximation of marginal likelihoods within MCMC without recognising this as a pseudo-marginal algorithm; hence, no access to results like Andreiu & Vihola (2012) [& 2014] on optimal choices for the estimator in the marginal likelihood estimation step (hint: the key is the acceptance ratio, not necessarily the variance! [as emphasised in Matti Vihola’s talk to the reading group a couple of weeks ago]).

Okay, not the only quibble, I also moan that they didn’t give any citations to my previous work advocating DPs in astronomy: e.g. ‘what we talk about when we talk about fields’ or ‘a semi-parametric Bayesian analysis of the quasar dataset‘! But, then again, if I get a citation to my ABC work from any of Hogg’s apparently upcoming ABC papers I’ll eat my hat …

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I’m thinking of offering a student project on ABC for gravitational microlensing. I will make sure to cite all of your papers. 😉