Today on astro-ph we were treated to a full article on uniform sampling within triangular boundary constraints where perhaps a paragraph, or a very short appendix, would have sufficed: http://arxiv.org/pdf/1308.0009.pdf . The context was for sampling from an uninformative prior on a parametric limb darkening curve under the constraints that the sampled parameters must produce an everywhere positive, monotonic output: these two conditions defining a triangle of allowed parameter space. Naturally, the necessary prior can be written as an uniform Dirichlet; the sampling from which the author shows to be more productive than sampling from, say, an enclosing square with rejection of the dis-allowed draws.

Surprisingly a good chunk of text is given to describing an algorithmic scheme from computer science for sampling from the uniform Dirichlet, though the most obvious (and more general) choice of drawing three gammas is not mentioned here. There’s also a silly comment about efficiency of sampling within these boundary constraints with MCMC or nested sampling … obviously if you were worried about computational efficiency you wouldn’t run your code on the problem with rejection of boundary regions: you’d transform your parameters to avoid this or over-parameterize your model (like everyone does for the weights of a mixture; cf. Cappe et al. 2003, Lee et al. 2008, etc. for guidance).

I don’t wake up in the morning intending to be an asshole, but somehow reading astro-ph just makes me this way! 🙂

On the other hand, if editors would send me astro-statistics papers to referee (rather than galaxy evolution ones) …

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Ohh … I forgot to add what I thought would have been a worthwhile paper on this subject: a non-parametric prior for limb darkening laws under the same regularization constraints!

“On the other hand, if editors would send me astro-statistics papers to referee (rather than galaxy evolution ones) …”

I feel your pain on that.