Characterizing the Sample Selection for Supernova Cosmology

TL;DR

This paper examines how sample selection criteria impact supernova-based cosmological parameter inference, highlighting the importance of numerical accuracy in likelihood calculations.

Contribution

It introduces toy models and Monte Carlo methods to quantify numerical errors in likelihood estimation for supernova cosmology.

Findings

Numerical errors depend on the number of Monte Carlo realizations.

Analytical likelihood calculation is only feasible for simple selection criteria.

The approach helps determine computational requirements for realistic models.

Abstract

Type Ia supernovae (SNe Ia) are used as distance indicators to infer the cosmological parameters that specify the expansion history of the universe. Parameter inference depends on the criteria by which the analysis SN sample is selected. Only for the simplest selection criteria and population models can the likelihood be calculated analytically, otherwise it needs to be determined numerically, a process that inherently has error. Numerical errors in the likelihood lead to errors in parameter inference. This article presents toy examples where the distance modulus is inferred given a set of SNe at a single redshift. Parameter estimators and their uncertainties are calculated using Monte Carlo techniques. The relationship between the number of Monte Carlo realizations and numerical errors is presented. The procedure can be applied to more realistic models and used to determine the computational and data management requirements of the transient analysis pipeline.