Bayesian evidence comparison for distance scale estimates

TL;DR

This paper introduces a Bayesian framework for selecting and comparing basis functions in cosmological distance scale estimation, allowing for more model-independent analysis of sky survey data.

Contribution

It presents a novel Bayesian method to determine the optimal number of basis functions and compare different basis sets for cosmological distance measurements.

Findings

Framework successfully applied to simulated data

Effective in comparing basis sets for distance estimation

Provides insights into prior dependence and belief updates

Abstract

Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the distance scale using templates that are more generic: the basis functions used are not explicitly tied to any one cosmological model. We describe a Bayesian framework for (i) determining how many basis functions to use and (ii) comparing one basis set with another. Our formulation provides intuition into how (a) one's degree of belief in different basis sets, (b) the fact that the choice of priors depends on basis set, and (c) the data set itself, together determine the derived constraints. We illustrate our framework using measurements in simulated datasets before applying it to real data.