The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and parameters). For most common utility functions, the expected utility is rarely available in closed form and requires a computationally expensive approximation which then needs to be maximised over the space of all possible designs. This hinders practical use of the Bayesian approach to find experimental designs. However, recently, a new utility called Fisher information gain has been proposed. The resulting expected Fisher information gain reduces to the prior expectation of the trace of the Fisher information matrix. Since the Fisher information is often available in closed form, this significantly simplifies approximation and subsequent identification of optimal designs. In this paper, it is shown that for exponential family models, maximising the expected Fisher information gain is equivalent to maximising an alternative objective function over a reduced-dimension space, simplifying even further the identification of optimal designs. However, if this function does not have enough global maxima, then designs that maximise the expected Fisher information gain lead to non-identifiablility.
翻译:贝叶西亚决定理论设计实验的方法涉及具体规定一种设计(所有可控变量的价值),以尽量扩大预期的效用功能(预测反应和参数的分布);对于大多数常见的效用功能,预期的效用很少以封闭形式提供,需要一种计算成本高昂的近似,从而需要在所有可能的设计空间上实现最大程度的接近。这妨碍了对巴伊西亚方法的实际使用,以寻找实验设计。然而,最近提出了一个新的效用,称为渔业信息增益。因此,预期的渔业信息增益将减少到对渔业信息矩阵追踪的预期值。由于渔业信息往往以封闭形式提供,因此这种资料大大简化了近似和随后确定最佳设计。在本文中显示,对于指数式家庭模型,尽量扩大预期的渔业信息增益相当于在缩小区域空间上实现替代目标功能的最大化,甚至进一步简化了最佳设计的确定。但是,如果这一功能不具备足够的全球最高标准,则会设计出尽可能扩大预期的渔业信息取得非机密性。