S U M M A R Y Statistical experimental design (SED) is the field of statistics concerned with designing experiments to obtain as much information as possible about a target of interest. SED algorithms can be divided into two categories: those that assume a linear or linearized relationship between measured data and parameters, and those that account for a fully nonlinear relationship. We compare the most commonly used linear method, Bayesian D-optimization, to two nonlinear methods, maximum entropy design and DN-optimization, in a synthetic seismological source location problem where we define a region of the subsurface in which earthquake sources are likely to occur. Example random sources in this region are sampled with a uniform distribution and their arrival time data across the ground surface are forward modelled; the goal of SED is to define a surface monitoring network that optimally constrains this set of source locations given the data that would be observed. Receiver networks so designed are evaluated on performance—the percentage of earthquake pairs whose arrival time differences are above a threshold of measurement uncertainty at each receiver, the number of prior samples (earthquakes) required to evaluate the statistical performance of each design and the SED compute time for different subsurface velocity models. We find that DN-optimization provides the best results both in terms of performance and compute time. Linear design is more computationally expensive and designs poorer performing networks. Maximum entropy design is shown to be effectively impractical due to the large number of samples and long compute times required.

中文翻译：

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全非线性源定位问题的实验设计：我应该选择哪种方法？

总结 统计实验设计 (SED) 是与设计实验有关的统计学领域，以获取有关感兴趣目标的尽可能多的信息。SED 算法可以分为两类：假设测量数据和参数之间存在线性或线性关系的算法，以及考虑完全非线性关系的算法。在合成地震源定位问题中，我们将最常用的线性方法贝叶斯 D 优化与两种非线性方法最大熵设计和 DN 优化进行比较，在该问题中我们定义了可能发生地震源的地下区域. 该区域的示例随机源以均匀分布采样，它们在地表上的到达时间数据被正向建模；SED 的目标是定义一个地表监测网络，在给定将要观察到的数据的情况下，以最佳方式限制这组源位置。对如此设计的接收器网络进行性能评估——到达时间差高于每个接收器测量不确定性阈值的地震对的百分比、评估每个设计的统计性能所需的先验样本（地震）数量以及 SED 计算不同地下速度模型的时间。我们发现 DN 优化在性能和计算时间方面都提供了最好的结果。线性设计的计算成本更高，并且设计的网络性能较差。由于需要大量样本和较长的计算时间，最大熵设计被证明实际上是不切实际的。