Zhou Xiaojie, Joseph Lawrence, Wolfson David B, Bélisle Patrick
The Procter & Gamble Company, 8700 Mason-Montgomery Road, Mason, Ohio, USA.
Biometrics. 2003 Dec;59(4):1082-8. doi: 10.1111/j.0006-341x.2003.00124.x.
Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A-optimality. We use this generalized A-optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A-optimality.
假设一组数据背后的真实模型是一组有限候选模型中的一个，并且该模型的参数估计是主要关注点。出于这个目标，最优设计必须依赖于所有可能模型上的损失函数。一种考虑模型不确定性的常用方法是对所有模型的损失进行平均；这就是所谓的劳特准则的基础。我们推广了劳特准则，并表明通过扩展贝叶斯A最优性的定义，它可以置于贝叶斯决策理论框架中。我们使用这种广义的A最优性在环境安全设定中找到最优设计点。在估计水污染问题中最小可检测痕量限值时，我们获得的最优设计与标准A最优性所建议的设计有很大不同。
