Hu Jianhua, Johnson Valen E
University of Texas M. D. Anderson Cancer Center, Houston, USA.
J R Stat Soc Series B Stat Methodol. 2008 Oct 14;71(1):143-158. doi: 10.1111/j.1467-9868.2008.00678.x.
Existing Bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set. In practice, this requirement limits the application of Bayesian model selection methodology. To overcome this limitation, we propose a new approach towards Bayesian model selection that uses classical test statistics to compute Bayes factors between possible models. In several test cases, our approach produces results that are similar to previously proposed Bayesian model selection and model averaging techniques in which prior distributions were carefully chosen. In addition to eliminating the requirement to specify complicated prior distributions, this method offers important computational and algorithmic advantages over existing simulation-based methods. Because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates, our method facilitates the selection of hyperparameter values through prior-predictive simulation.
现有的贝叶斯模型选择程序要求在选择集中的每个模型中出现的参数上指定先验分布。在实践中，这一要求限制了贝叶斯模型选择方法的应用。为了克服这一限制，我们提出了一种新的贝叶斯模型选择方法，该方法使用经典检验统计量来计算可能模型之间的贝叶斯因子。在几个测试案例中，我们的方法产生的结果与先前提出的贝叶斯模型选择和模型平均技术相似，在这些技术中先验分布是经过精心选择的。除了消除指定复杂先验分布的要求外，该方法还比现有的基于模拟的方法具有重要的计算和算法优势。由于对于给定的样本量和指定的协变量数量，很容易评估该程序的操作特性，我们的方法通过先验预测模拟促进了超参数值的选择。
