Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
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DOI：
10.1214/16-sts576
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发表时间：
2017-02-01
影响因子：
5.7
通讯作者：
Sorbye, Sigrunn H.
中科院分区：
文献类型：
--
作者：
Simpson, Daniel;Rue, Havard;Sorbye, Sigrunn H.
在本文中，我们引入了一个新的概念，用于构建先验分布。我们利用了许多模型组件所固有的自然嵌套结构，它将模型组件定义为基础模型的灵活扩展。适当的先验定义为惩罚的复杂性引起的偏离简单的基础模型，并制定后，输入的用户定义的缩放参数的模型组件，无论是在单变量和多变量的情况下。这些先验是不变的repara-rameterisation，有一个自然的连接到杰弗里斯的先验，旨在支持奥卡姆剃刀，似乎有很好的鲁棒性，所有这些都是非常可取的，并允许我们使用这种方法来定义默认的先验分布。通过实例和理论结果，我们证明了这种方法的适当性，以及它如何可以应用于各种情况。
In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to repa-rameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.