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arXiv 2102.10671astro-ph.COgr-qc
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宇宙学中模型选择方法的比较

Comparison between different methods of model selection in cosmology

Mehdi Rezaei, Mohammad Malekjani

备注：
12 pages, 3 figures, PUBLISHED IN EPJP. arXiv admin note: text overlap with arXiv:1510.00547 by other authors
发表信息：
Eur. Phys. J. p (2021) 136:219
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摘要：

在宇宙学中有几种模型选择的方法，它们至少有两个主要目标，即找到正确的模型或很好地预测。在这项工作中，我们讨论了通过研究著名的模型选择方法，如赤池信息准则（AIC），贝叶斯信息准则（BIC），偏差信息准则（DIC）和贝叶斯证据，这些不同的目标是如何在每个范式追求。我们还采用了另一种在宇宙学文献中较少见到的模型选择方法，即交叉验证方法。利用这些方法，我们将比较宇宙学中的两种不同情况，$Λ$ CDM模型和动力学暗能量。我们表明，每种方法往往在模型选择不同的结果。虽然BIC和贝叶斯证据推翻了具有2或3个额外自由度的动力学暗能量场景，DIC和交叉验证方法更喜欢这些动力学模型而不是$Λ$ CDM模型。假设不同分析的数值结果，并结合宇宙学和统计方面的问题，我们提出交叉验证作为一个有趣的方法，在宇宙学模型选择，可以导致不同的结果相比，通常的模型选择方法。

英文摘要：

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, $Λ$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.

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