2019/11/27 by Thomas J. Loredo, M. Hendry, Loredo, Thomas J. +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · Social Sciences · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Insurance, Mortality, Demography, Risk Management #astro-ph.IM #stat.AP
paper · pdf · doi:10.48550/arxiv.1911.12337
33 pages, 5 figures
arxiv created 2019/11/27 · openalex publication_date 2019/11/27 · arxiv updated 2019/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and the literature on corrections for Malmquist and Eddington bias. From the perspective of modern statistics, such corrections arise naturally in the context of multilevel models, particularly in Bayesian treatments of such models: hierarchical Bayesian models. We survey some key lessons from hierarchical Bayesian modeling, including shrinkage estimation, which is closely related to traditional corrections devised by astronomers. We describe a framework for hierarchical Bayesian modeling of cosmic populations, tailored to features of astronomical surveys that are not typical of surveys in other disciplines. This thinned latent marked point process framework accounts for the tie between selection (detection) and measurement in astronomical surveys, treating selection and measurement error effects in a self-consistent manner.