An ANOVA model for dependent random measures
An ANOVA model for dependent random measures
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DOI：
10.1198/016214504000000205
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发表时间：
2004-03-01
影响因子：
3.7
通讯作者：
MacEachern, SN
中科院分区：
文献类型：
--
作者：
De Iorio, M;Müller, P;MacEachern, SN
我们考虑相关随机概率分布的相依非参数模型。例如，随机分布可以由指示临床试验中的治疗水平的分类协变量来索引，并且可以表示在相应治疗组合下的随机效果分布。我们提出了一个模型，它以方差分析(ANOVA)的方式描述了随机分布之间的相关性。我们定义了一个概率模型，使得每个随机度量边际上服从Dirichlet过程(DP)，并使用依赖的Dirichlet过程来定义相关随机度量之间的期望相关性。可替换地，所得到的概率模型可以被描述为具有未知混合度量上的DP先验的ANOVA模型的混合。该方法的主要特点是易于解释和计算简单。由于该模型遵循标准的ANOVA结构，因此解释和推理与ANOVA模型的约定相似。这包括主要影响的概念。互动、对比等。当然，这些类比仅限于结构和解释。推断的实际对象是随机分布，而不是标准ANOVA模型中未知的正态均值。除了解释和模型结构外，该方法的另一个重要特点是易于后验模拟。由于该模型可以改写为方差分析模型的DP混合模型，因此它继承了标准DP混合模型的所有计算优势。这包括用于后验模拟的高效吉布斯抽样方案的可用性，以及即使是高维应用的实施的简便性。实现后验模拟的复杂性是--至少在概念上--与维度无关。
We consider dependent nonparametric models for related random probability distributions. For example, the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations. We propose a model that describes dependence across random distributions in an analysis of variance (ANOVA)-type fashion. We define a probability model in such a way that marginally each random measure follows a Dirichlet process (DP) and use the dependent Dirichlet process to define the desired dependence across the related random measures. The resulting probability model can alternatively be described as a mixture of ANOVA models with a DP prior on the unknown mixing measure. The main features of the proposed approach are ease of interpretation and computational simplicity. Because the model follows the standard ANOVA structure, interpretation and inference parallels conventions for ANOVA models. This includes the notion of main effects. interactions, contrasts, and the like. Of course, the analogies are limited to Structure and interpretation. The actual objects of the inference are random distributions instead of the unknown normal means in standard ANOVA models. Besides interpretation and model structure, another important feature of the proposed approach is ease of posterior simulation. Because the model can be rewritten as a DP mixture of ANOVA models, it inherits all computational advantages of standard DP mixture models. This includes availability of efficient Gibbs sampling schemes for posterior simulation and ease of implementation of even high-dimensional applications. Complexity of implementing posterior simulation is-at least conceptually-dimension independent.