Bayesian model selection using encompassing priors
Bayesian model selection using encompassing priors
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DOI：
10.1111/j.1467-9574.2005.00279.x
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发表时间：
2005-02-01
影响因子：
1.5
通讯作者：
Hoijtink, H
中科院分区：
文献类型：
--
作者：
Klugkist, I;Kato, B;Hoijtink, H
本文讨论了可以使用模型参数之间的不等约束来指定的模型的贝叶斯选择。引入了包含先验的概念，即无约束模型的先验分布，由该先验分布可以得到约束模型的先验分布。结果表明，包络模型和约束模型的贝叶斯因子有很好的解释：它是包络模型的先验分布和后验分布与约束模型一致的比例。研究还表明，对于一类特定的模型，基于包含性先验的选择将呈现一个几乎客观的选择过程。文章最后给出了三个例子：有序均值的方差分析、有序赔率的列联表分析和有序斜率的多水平模型。
This paper deals with Bayesian selection of models that can be specified using inequality constraints among the model parameters. The concept of encompassing priors is introduced, that is, a prior distribution for an unconstrained model from which the prior distributions of the constrained models can be derived. It is shown that the Bayes factor for the encompassing and a constrained model has a very nice interpretation: it is the ratio of the proportion of the prior and posterior distribution of the encompassing model in agreement with the constrained model. It is also shown that, for a specific class of models, selection based on encompassing priors will render a virtually objective selection procedure. The paper concludes with three illustrative examples: an analysis of variance with ordered means; a contingency table analysis with ordered odds-ratios; and a multilevel model with ordered slopes.