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Demographic studies of cosmic populations must contend with measurementerrors and selection effects. We survey some of the key ideas astronomers havedeveloped to deal with these complications, in the context of galaxy surveysand the literature on corrections for Malmquist and Eddington bias. From theperspective of modern statistics, such corrections arise naturally in thecontext of multilevel models, particularly in Bayesian treatments of suchmodels: hierarchical Bayesian models. We survey some key lessons fromhierarchical Bayesian modeling, including shrinkage estimation, which isclosely related to traditional corrections devised by astronomers. We describea framework for hierarchical Bayesian modeling of cosmic populations, tailoredto features of astronomical surveys that are not typical of surveys in otherdisciplines. This thinned latent marked point process framework accounts forthe tie between selection (detection) and measurement in astronomical surveys,treating selection and measurement error effects in a self-consistent manner.

Multilevel and hierarchical Bayesian modeling of cosmic populations