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 depends 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.
翻译:贝叶斯语推论用于模型选择的运用如今非常普遍。在这个框架中,模型通过其边际可能性或商数来比较,称为贝叶斯因素。但是,边际可能性取决于先前的选择。对于模型选择,即使分散的前题实际上也会非常丰富,与参数估计问题不同。此外,如果先前不适当,相应模型的边际可能性是不确定的。在这项工作中,我们讨论了边际可能性的先前敏感性及其在模型选择中的作用。我们还评论了使用非信息规范前题的问题,这是实践中非常常见的选择。我们讨论了一些实用的建议,并介绍了文献中为设计模型选择目标前题而提出的许多可能的解决办法。其中一些还允许使用不适当的前题。还介绍了边际可能性方法与众所周知的信息标准之间的联系。我们通过说明性数字实例来描述主要问题和可能的解决办法,并提供了一些相关的代码。其中之一是在外行星网探测上实际应用。