Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
复制标题
在贝叶斯非参数模型中建模协变量时对预测的影响。
DOI：
10.1080/15598608.2013.772811
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发表时间：
2013
影响因子：
0.6
通讯作者：
Stewart,ClintonF
中科院分区：
文献类型：
--
作者：
Cruz-Marcelo,Alejandro;Rosner,GaryL;Müller,Peter;Stewart,ClintonF
在生物医学研究中，描述引起观察的生物过程并对未来的观察做出预测通常是令人感兴趣的。贝叶斯非参数方法提供了一种执行贝叶斯推理的方法，对限制性参数模型的假设尽可能少。文献中有几个关于扩展贝叶斯非参数模型以包括对协变量的依赖性的建议。在这篇文章中，我们考察了在一类贝叶斯非参数模型中加入协变量对拟合和预测性能的影响，主要方法有两种：一种是在权重中，另一种是在离散随机概率度量的位置上。我们表明，在贝叶斯非参数模型中加入连续协变量的不同策略在用于预测时会导致很大的差异，即使它们会导致其他类似的后验推断。当一个人需要预测密度时，比如在优化设计中，这个密度是混合的，最好是使权重依赖于协变量。我们通过一个模拟的数据例子和一个想要确定在儿科肿瘤学中使用的抗癌药物的最佳剂量的应用来展示这些观点。
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparamric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.