On the safe use of prior densities for Bayesian model selection

IF 4.4 2区 数学 Q1 STATISTICS & PROBABILITY
F. Llorente, Luca Martino, E. Curbelo, J. Lopez-Santiago, D. Delgado
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引用次数: 6

Abstract

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depend on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well‐known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real‐world application on exoplanet detection.
贝叶斯模型选择中先验密度的安全使用
贝叶斯推理在模型选择中的应用在当今非常流行。在这个框架中,模型通过它们的边际可能性或商进行比较,称为贝叶斯因子。然而,边际可能性取决于先前的选择。对于模型选择,与参数估计问题不同,即使是扩散先验实际上也可以提供非常丰富的信息。此外,当先验不合适时,相应模型的边际似然是不确定的。在这项工作中,我们讨论了边际似然的先验敏感性问题及其在模型选择中的作用。我们还评论了无信息先验的使用,这是实践中非常常见的选择。讨论了一些实用的建议,并描述了文献中提出的许多可能的解决方案,以设计用于模型选择的目标先验。其中一些还允许使用不适当的先验。还介绍了边际似然法和众所周知的信息准则之间的联系。我们通过举例说明了主要问题和可能的解决方案,并提供了一些相关的代码。其中一项涉及到系外行星探测的真实应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.20
自引率
0.00%
发文量
31
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