I noticed this paper by Romano et al. (2014), which has been accepted to A&A, claiming to have derived a Bayesian approach for estimating the duty cycle (DC; the proportion of time spent in one of two possible states [on/off, excited/non-excited, etc]) of a variable source. Given that variable sources are often periodic and are observed over a range of times and durations I expected to see a fairly sophisticated analysis: perhaps with a flexible family of periodic and quasi-periodic candidate models, or maybe with a two-state continuous time Markov process model taking into account the full observational sequence. But no, what is proposed is surely the most trivial case, equivalent to the (unstated) assumption that the observational dataset consists of N observations of equal duration near-uniformly spaced over a period of time covering many effective periods if the source is (perhaps quasi-)periodic, such that at first blush the problem can be treated as inferring the population proportion from binomial count data. Under these ridiculously simplifying assumptions the authors repeat briefly the basics of Bayesian inference for binomial data which I have already described in Cameron (2010), “On the estimation of confidence intervals for binomial population proportions in astronomy: The simplicity and superiority of the Bayesian approach”. The only additional suggestion they give is to assign shared hyperparameters for the Beta prior on the unknown population proportion for each source, which lends the problem a hierarchical structure likely to bring about some positive Bayesian shrinkage: although it is not even clear that the authors are suggesting a fully Bayesian hierarchical fit in part because they give an arbitrary requirement of 50 or more objects in the sample to apply this technique and don’t mention hyperpriors.
Again, sad to see that this got through review at A&A. Not sad to see that one of the authors has an affiliation to the ISDC in Geneva: I once emailed Stephane Udry to ask whether he’d consider supporting me in an SNSF fellowship application to work on astrostatistics problems at the ISDC (embedded with the U. Geneve astronomy department) and he didn’t even deign to reply. Thanks, champ!