Astro ph round up …

Just a quick brain dump after flicking through today’s astro ph.  First, there’s a bit of a face-palm by Schlaufmam, who highlights (correctly) the usefulness of logistic regression for modelling binomial data (here exoplanet frequencies as a function of metallicities), but then declares (incorrectly) that the intercept, beta_0, to have no meaningful interpretation.  In fact it has a very meaningful interpretation as the log-odds ratio when the predictor variable(s) is(are) zero.  Rather than estimating the intercept and slope simultaneously (and hence parsimoniously) via glm in R Schlaufmam adopts the unconventional strategy of taking the mean of his data points with (relative log) metallicities near zero, followed by bootstrapping for the uncertainty. I’d also point out that for Bayesians the probit regression model is always worth considering: it describes a very similar sigmoid curve to logistic regression but its conjugacy to normal priors allows for fast Gibbs sampling of its posterior.  Wikipedia has all the details on this.

Fouesneau et al have a paper presenting mass, age, and reddenings for stellar clusters in Andromeda, derived with a simple Bayesian procedure that should be robust against the effects of stochastic sampling of the IMF at low masses.  Importantly, with regard to my disregard for the Pflamm-Altenburg et al work on this topic, there is no evidence in their catalog for a galactocentric radius dependence in the upper mass of young star clusters.  Indeed one can download the full catalog from the source files of their astro ph submission, select the 125 clusters with best fitting ages less than 0.1 Gyr and masses greater than 10^2.8 solar masses, run a quantile regression on say the 95th upper mass quantile with declination a (good) proxy for galactocentric sample here, and voila: a completely rubbish p-value of 0.5.

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