论文标题
使用Fisher信息获得实验设计的特性
Properties of using Fisher information gain for Bayesian design of experiments
论文作者
论文摘要
实验设计的贝叶斯决策理论方法涉及指定设计（所有可控变量的值），以最大程度地提高预期效用函数（对响应和参数的分布的期望）。对于最常见的实用程序功能，预期的实用程序很少以封闭形式获得，并且需要一个计算昂贵的近似值，然后需要在所有可能的设计的空间中最大化。这阻碍了贝叶斯方法的实际使用来寻找实验设计。但是，最近，提出了一个名为Fisher信息增益的新公用事业。由此产生的预期Fisher信息增益减少到Fisher信息矩阵的痕迹的先前预期。由于Fisher信息通常以封闭形式获得，因此这大大简化了最佳设计的近似和随后的识别。在本文中，结果表明，对于指数式的家庭模型，最大化预期的Fisher信息增益相当于在减少差异空间上最大化替代目标函数，从而进一步简化了最佳设计的识别。但是，如果此功能没有足够的全球最大值，则设计最大化预期的Fisher信息增益会导致非识别性。
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.
