Modelling the multiplicity of planets around M dwarfs …

I noticed this paper on astro ph today by Ballard & Johnson presenting a statistical model for inferring the multiplicity of planets around M dwarf hosts using a small-ish sample of KOIs (Kepler objects of interest) distributed amongst 106 stars.  The base model is for a Poisson distribution of planets thinned by an observational selection function; the likelihood evaluation of which is achieved via simulation in a style akin to the pseudo-marginal method without MCMC (i.e. using a brute-force grid over the two free parameters instead).  However, a simple posterior predictive check reveals that the base model cannot comfortably reproduce the observed distribution of planet multiplicities: in particular, there appears to be a surplus of single planet systems in the observed data.  Hence, the authors also present results for a one-inflated (instead of zero-inflated!) Poisson mixture model which is sufficiently flexible.  The only reservation I have (apart from a consistent typo on the exponent of the Poisson likelihood in the manuscript) is that there are various other ways one could well think to account for non-Poissonian behaviour here—the most obvious being to use a Poisson-Gamma / Negative Binomial model—which perhaps ought to be compared and discussed in terms of both fits and physical plausibility.  In any case it is worth stressing that future studies aiming to regress the mean planet multiplicity against candidate predictors (e.g. stellar metallicity / age) need bear in mind this over-dispersion: perhaps to try a negative binomial regression from the GLM family as opposed to (or in comparison with) a Poisson regression (cf. the first round of COIN papers discussed a couple of blog posts below).

On my reading list also from this week is the pair of promising-looking papers by Cornish & Littenberg on BayesWave / BayesLine: a two-part algorithm for gravitational wave detection featuring a finite mixture model for non-continuum events fit with a reversible jump MCMC procedure.

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