Comparison between different methods of model selection in cosmology

• Published in: European physical journal plus Vol. 136; no. 2; p. 219
• Main Authors: Rezaei, Mehdi, Malekjani, Mohammad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021; Springer Nature B.V
• Subjects: Applied and Technical Physics; Approximation; Atomic; Bayesian analysis; Complex Systems; Condensed Matter Physics; Cosmology; Criteria; Dark energy; Dynamic models; Mathematical and Computational Physics; Methods; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01200-w

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 is less seen in cosmological literature, the cross-validation method. Using these methods, we will compare two different scenarios in cosmology: Λ 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 Λ 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.