I had a conversation today with Adrian Price-Whelan (Flatiron) about doing population inferences with our catalog of binary companions from APOGEE. We have two options: Either build a hierarchical Bayesian model, with all the likelihoods that we have created for every star, whether or not it shows good evidence for a companion, or else we perform a set of injection/recovery tests to see what stars show good evidence for what kinds of companions and perform a frequentist populations analysis given those tests. You might think that there is a right answer to this, but there isn't: The different approaches involve different kinds of operations, and have different sensitivities to input assumptions.
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