Informed total-error-minimizing (item) priors: interpretable cosmological parameter constraints despite complex nuisance effects

Abstract

Modern physical cosmology aims to understand the physics of the universe, i.e., the kinematical and dynamical processes, the contents, the structure, and the cosmic origin and evolution. To fully understand it, the cosmological probes must be analyzed with the latest statistical knowledge possible, specifically due to the forthcoming entire sky surveys. The upcoming datasets will require us to consider physical models of smaller scales and higher-order statistics than the usually studied in cosmology. Because of that, we call this epoch the era of precision cosmology. A particular challenge arises when models increase their complexity by adding parameters without constraining their preliminary information for an accurate Bayesian analysis: the prior volume effect. This effect can lead cosmological interpretations to radical wrong assumptions and tensions that might not even exist. Our proposal includes a systematic framework that derives informed and total error minimizing prior distributions to nuisance parameters from a set of possible nuisance effects. In this work, we present a thorough literature review of both cosmology and statistics to set the investigation s basis. The former includes the basics of physical cosmology and the cosmic structure formation in Chapters 2 and 3, respectively. Comprehensive reviews and discussions around the use of probabilities and statistical inference are included in Chapters 4 and 5, respectively. We incorporate an examination of the German tank problem in Chapter 6 and remark on its importance relative to cosmological analysis. The main scientific result is shown in Chapter 7, where we propose a method to correct the prior volume effect through a simulated likelihood analysis. We test it with the shot-noise models from the density split statistics framework [1, 2] with data from the Dark Energy Survey (DES) Y1. This novel method extends the approach of the likelihood analysis, not limited to observational cosmology, but to all the areas in which Bayesian analyses are taken into account.