Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design
Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design
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DOI：
10.1029/2010wr010137
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发表时间：
2012-02-01
影响因子：
5.4
通讯作者：
Nowak, W.
中科院分区：
文献类型：
--
作者：
Leube, P. C.;Geiges, A.;Nowak, W.
将水（地质）数据（例如水头和示踪数据）纳入（地下）流动和传输的随机模型中有助于减少预测的不确定性。由于调查活动的资金限制，建模或预测目标的信息需求应该有效且合理地得到满足。最佳设计技术在一组研究策略中找到最好的一个。他们在数据收集之前优化数据对预测置信度或相关目标的预期影响。我们引入了一种新的优化设计方法，称为 PreDIA(gnosis)（Preposterior Data Impact Assessor）。 PreDIA 在完全贝叶斯、广义、灵活和准确的框架内导出数据效用的相关概率分布和度量。它通过边缘化未知数据值的效用度量，将自举过滤器（BF）和相关框架扩展到最优设计。 PreDIA 是一种严格形式化的信息处理方案，无需线性化。它可与任意仿真工具配合使用，提供有关测量类型（线性、非线性、直接、间接）的充分灵活性，允许任何所需的任务驱动公式，并且可以通过贝叶斯地质统计学和模型平均来解释各种不确定性来源（例如，异质性、地质统计假设、边界条件、测量值、模型结构不确定性、一大类模型误差）。现有方法无法同时提供这些关键优势，而我们的方法以相对较高的计算成本获得了这些优势。我们在地下输运的综合示例中展示了 PreDIA 相对于传统线性化方法的适用性和优势。在示例中，我们表明，对于将零相关性与统计独立性混淆的线性化方法来说，信息数据通常是不可见的。因此，PreDIA 通常会带来更好的采样设计。最后，我们扩展我们的示例以特别强调概念模型不确定性的考虑。
Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.