I had a productive email exchange with Miguel Cervino (who wrote this review of the challenges for stellar population parameter inference under the stochastic effects of IMF sampling in low mass star clusters) regarding the potential for ABC in this field. While the existing strategies (e.g. Fouesneau & Lancon 2010) can be thought of a primitive ABC using a pre-compiled library of simulations, there seems to be much potential for advanced ABC methods here in the case of partially resolved clusters: i.e. where the likelihood of observing a given integrated light SED along with the specific SEDs of a few of the cluster’s most luminous stars is presumably both intractable and non-Gaussian. Nice!
I’ve also been reading up on the INLA (Integrated Nested Laplace Approximation) method for extracting marginals and hyperparameter posteriors from latent Gaussian models with sparse covariance matrices. The computational speed ups compared to contemporary MCMC approaches can be quite overwhelming. Given the speed ups my colleagues at Oxford Zoology have seen in fitting their large scale geospatial models of malaria prevalence (rivalling cosmological modelling in scale) I could well imagine INLA allowing for extraction of correlation function parameters from e.g. the SDSS galaxy distribution in just hours on a standard desktop, as opposed to weeks on a cluster with MCMC!
Unlucky news today was that one of my coauthor papers was rejected by a stats journal with 20% acceptance rate. As so often happens the experience was soured by a strangely hostile reviewer (one of two reviewers) who couldn’t see the applicability of our work to his/her scientific field (for which it was never intended) and therefore couldn’t see any use for it in ours (or any others)! Also he/she recommended we consult Paper X to see how a statistics paper should be written when in fact we cite Paper X in our manuscript and give a correction/extension to one of Paper X’s theorems (which the authors of Paper X agree with)! Seriously?! You can’t make this stuff up.