A Bayesian indirect inference for the binary fraction in Leo II …

A recent arXival by Spencer et al. presents a Bayesian analysis of radial velocity data for the binary fraction in (the ultra faint dwarf galaxy) Leo II in which the inference proceeds by comparison of mock datasets against the observed data.  In this particular case the methodology ends up corresponding to a Bayesian indirect inference algorithm (e.g. Drovandi et al., Creel et al.) in which the summary statistic is the counts in bins of the beta statistic (observational error weighted squared pairwise difference between radial velocities in consecutive observations) and its auxiliary model is the skewed Normal (independent across bins).  In principle one could perform an ordinary Bayesian analysis of this data under a hierarchical model (which would also yield predictions for the binarity or otherwise of each star in the sample) but fitting might (? relative to the potential for contraction of the posterior) be overly time consuming due to the dimensionality and shape of the joint posterior.  Instead the indirect inference approach here is straightforwards to implement targeting the binary fraction directly, and a further set of input-output simulations reassure that the posterior median is effectively an unbiased estimator for the true binary fraction.

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