Comparison between different methods of model selection in cosmology

TL;DR

This paper compares various model selection methods in cosmology, including AIC, BIC, DIC, Bayesian evidence, and cross-validation, highlighting their differing conclusions when applied to ΛCDM and dynamical dark energy models.

Contribution

It introduces cross-validation as a less common but promising model selection method in cosmology and compares its results with traditional criteria.

Findings

BIC and Bayesian evidence favor ΛCDM over dynamical dark energy.

DIC and cross-validation prefer dynamical dark energy models.

Different methods can lead to contrasting model selection outcomes.

Abstract

There are several methods for model selection in cosmology which have at least two major goals, that of finding the correct model or predicting well. In this work we discuss through a study of well-known model selection methods like Akaike information criterion (AIC), Bayesian information criterion (BIC), deviance information criterion (DIC) and Bayesian evidence, how these different goals are pursued in each paradigm. We also apply another method for model selection which less seen in cosmological literature, the Cross-validation method. Using these methods we will compare two different scenarios in cosmology, $\Lambda$CDM model and dynamical dark energy. We show that each of the methods tends to different results in model selection. While BIC and Bayesian evidence overrule the dynamical dark energy scenarios with 2 or 3 extra degree of freedom, the DIC and cross-validation method prefer these dynamical models to $\Lambda$CDM model. Assuming the numerical results of different analysis and combining cosmological and statistical aspects of the subject, we propose cross-validation as an interesting method for model selection in cosmology that can lead to different results in comparison with usual methods of model selection.