Advertising the second (and final) paper in my series on the (lack of) evidence for cosmic variation of the fine structure constant. The purpose of this one is not simply to flog a dead horse, but rather to demonstrate a very neat way to carry out the flogging! 🙂 In brief, we (myself & my supervisor at QUT, Tony Pettitt) show how our (for-most-but-obviously-not-for-every-problem-under-the-sun-) preferred framework for Bayesian model selection—namely, marginal likelihood estimation via reverse logistic regression / biased sampling, followed by prior-sensitivity analysis via importance sample reweighting—extends naturally to problems in non-standard domains, such as that of semi-parametric error models with (mixture of) Dirichlet process priors. The (apparent) difficulty being that the familiar case of Riemann integration over probability density ratios becomes Lebesgue integration over Radon-Nikodym derivatives of probability measures. Plus we highlight some key similarities between unexplained error terms in astronomy and clinical meta-analysis (with the hope of stimulating some cross-disciplinary thinking in this regard).
The preprint on astro-ph: http://arxiv.org/abs/1309.2737