Coping With Conceptual Uncertainty: A Maximum Likelihood Bayesian Model Averaging Approach

应对概念不确定性：最大似然贝叶斯模型平均方法

• 批准号: 0407123
• 负责人: Shlomo Neuman
• 金额: $ 36.44万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0407123&HistoricalAwards=false
• 关键词: Coping; Conceptual; Uncertainty; Maximum; Likelihood

0407123NeumanGoal: Allow hydrologists to cope quantitatively with conceptual model uncertainty via a well-founded andwell-researched methodology, incorporating maximum likelihood parameter estimation in a multimodel Bayesian updating framework, which is feasible to implement in practice.Objectives: (1) To firm up the theoretical basis of a Maximum Likelihood Bayesian Model Averaging(MLBMA) method recently proposed by the PI (Neuman, 2002, 2003) for the rendering of optimum hydrologic predictions by means of several competing models and the assessment of their joint predictive uncertainty. (2) To implement, explore and demonstrate MLBMA on hydrogeologic data, distributed in three-dimensional space and time, collected earlier in unsaturated fractured rock at the Apache Leap Research Site (ALRS) in central Arizona. The Problem: Hydrologic analyses typically rely on a single conceptual-mathematical model of geologic or watershed makeup and corresponding hydrologic processes. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. This is true regardless of the quantity and quality of available data. Predictions and analyses of uncertainty based on a single hydrologic concept are prone to statistical bias (by committing a Type II error through reliance on an inadequate model) and underestimation of uncertainty (by committing a Type I error through under sampling of the relevant model space). The bias and uncertainty that result from reliance on an inadequate conceptual-mathematical model are often much larger than those introduced through an inadequate choice of model parameter values. Yet most hydrologic uncertainty analyses ignore the former and focus exclusively on the latter. This often leads to overconfidence in the predictive capabilities of the model, which the available hydrologic data seldom justify. Indeed, critiques of hydrologic analyses and scientific/regulatory/legal challenges to them typically focus on the validity of the underlying conceptual (and by implication mathematical) model. Existing method of dealing with the problem, most notably the Generalized Likelihood Uncertainty Estimation (GLUE) approach of Beven and Binley (1992; see alsoBeven and Freer, 2001) are, in the PIfs view, useful but not necessarily optimal for the purpose. There is a need for an innovative approach to the problem that rests on rigorous theory and is feasible to implement in practice. Approach: Under Objective 1 we propose to firm up the theoretical basis of MLBMA by exploringtheoretically and through synthetic numerical studies (a) the accuracy and computational feasibility of MLBMA in comparison to Bayesian Model Averaging (BMA) implemented via Markov Chain Monte Carlo simulation (Hoeting et al., 1999); (b) the impact that availability or lack of prior hydrologic parameter measurements have on this comparison; (c) the difference between computing posterior model probabilities using Kashyap fs (1982) Bayesian information criterion KIC (Neuman, 2002, 2003) versus the asymptotic Bayesian criterion BIC (proposed by Raftery, 1993) or non-Bayesian information theoretic criteria such as Akaike fs (1974) AIC (proposed by Burnham and Anderson, 2002); (d) the unresolved issue of how to assign prior probabilities to various models; and (e) the rate at which the sensitivity of posterior parameter estimates and model probabilities to the choice of prior parameter andmodel probabilities diminishes with the information content (quantity and quality) of hydrologic data. Some of these same issues will also be addressed vis-a-vis real data under Objective 2. Objective 2 is to implement, explore and demonstrate the predictive capabilities of MLBMA on hydrogeologic data collected earlier at the ALRS. These include air permeability and air-filled porosity data from pneumatic injection tests in 1-m-length intervals along six vertical and inclined boreholes at the site, and transient pressure data from cross-hole pneumatic injection tests in these and ten additional boreholes. The data represent largely a continuum of interconnected fractures. Their analysis will be conducted in three stages. At Stage 1 we propose to consider alternative geological-geostatistical models of how the 1-m-scale log permeability ()10 log k and log porosity ()10 log data vary in space, based solely on 1-m-scale measurements. At Stage 2, we will examine the extent to which a subset of these models, as well as BMA and MLBMA, are capable of predicting air flow between boreholes during cross-hole tests at the site basedsolely on prior information about lo , 10 g k 10 log and alternative representations of forcing terms. The prior information will consist of measurements, statistics, geological-geostatistical models, projections and projection covariances of these quantities across a domain containing all boreholes, established at Stage 1. At Stage 3 we propose to calibrate (via ML) airflow models having alternative parameter structures against pressure data observed during one cross-hole test at the ALRS and examine their ability, as well as that of MLBMA, to predict pressures observed during other such (validation) tests. The cross-hole tests will be selected so that injection takes place into a different borehole in each of them.Intellectual Merit and Broad Impacts: A solid theory and a practical methodology of rendering optimumhydrologic predictions and an assessment of predictive uncertainty that account jointly for uncertainties in model structure (conceptual-mathematical frameworks) and parameters. The approach applies to a broad range of models representing natural processes in ubiquitously open and complex earth and environmental systems. Results will bedisseminated broadly to researchers and practitioners through various means.

0407123NeumanGoal：允许水文学家通过一个有充分根据和充分研究的方法定量地处理概念模型的不确定性，在多模型贝叶斯更新框架中纳入最大似然参数估计，这在实践中是可行的。目的：(1)巩固PI （Neuman, 2002,2003）最近提出的最大似然贝叶斯模型平均（MLBMA）方法的理论基础，该方法通过几种相互竞争的模型和评估它们的联合预测不确定性来绘制最佳水文预测。(2)对亚利桑那州中部Apache Leap Research Site （ALRS）早期采集的非饱和裂隙岩石中分布在三维空间和时间上的水文地质数据进行MLBMA的实现、探索和论证。问题：水文分析通常依赖于地质或流域组成和相应水文过程的单一概念数学模型。然而，水文环境是开放和复杂的，使得它们容易有多种解释和数学描述。无论可用数据的数量和质量如何，这都是正确的。基于单一水文概念的不确定性预测和分析容易出现统计偏差（由于依赖不充分的模型而导致第二类误差）和对不确定性的低估（由于相关模型空间的抽样不足而导致第一类误差）。依赖不适当的概念数学模型所产生的偏差和不确定性，往往比不适当选择模型参数值所带来的偏差和不确定性要大得多。然而，大多数水文不确定性分析忽略了前者，而只关注后者。这往往导致对模型预测能力的过度自信，而现有的水文数据很少能证明这一点。事实上，对水文分析的批评和对它们的科学/监管/法律挑战通常集中在潜在概念（以及隐含的数学）模型的有效性上。在pif看来，处理这个问题的现有方法，最著名的是Beven和Binley（1992；另见Beven和Freer， 2001）的广义似然不确定性估计（GLUE）方法是有用的，但不一定是最优的。需要一种创新的方法来解决这个问题，这种方法建立在严谨的理论基础上，在实践中是可行的。方法：在目标1中，我们建议通过理论探索和综合数值研究来巩固MLBMA的理论基础(a)与通过马尔可夫链蒙特卡罗模拟实现的贝叶斯模型平均（BMA）相比，MLBMA的准确性和计算可行性（Hoeting等，1999）；(b)先前有无水文参数测量对这种比较的影响；(c)使用Kashyap fs（1982）贝叶斯信息准则KIC （Neuman, 2002, 2003）计算后验模型概率与使用渐近贝叶斯准则BIC （Raftery, 1993）或Akaike fs (1974) AIC （Burnham and Anderson, 2002）等非贝叶斯信息理论准则之间的差异；(d)未解决的如何为各种模型分配先验概率的问题；(e)后验参数估计和模型概率对先验参数和模型概率选择的敏感性随水文数据的信息量（数量和质量）而降低的速率。其中一些问题也将在目标2下针对实际数据进行讨论。目标2是实施、探索和证明MLBMA对早期ALRS收集的水文地质数据的预测能力。这些数据包括在现场沿6个垂直和倾斜井眼进行的1米长度的气动注入测试的透气性和充气孔隙度数据，以及在这些井眼和另外10个井眼进行的跨井气动注入测试的瞬态压力数据。这些数据在很大程度上代表了相互连接的连续裂缝。他们的分析将分三个阶段进行。在第一阶段，我们建议考虑替代的地质-地质统计模型，即1米尺度的测井渗透率（）10 log k和测井孔隙度（）10测井数据如何在空间上变化，仅基于1米尺度的测量。在第二阶段，我们将检查这些模型的子集，以及BMA和MLBMA，在多大程度上能够仅基于关于lo， 10 g k 10 log的先验信息和强迫项的替代表示来预测现场交叉孔试验期间钻孔之间的空气流动。先前的信息将包括测量、统计、地质-地质统计模型、预测和预测协方差，这些量横跨一个区域，包括在第一阶段建立的所有钻孔。在第3阶段，我们建议（通过ML）根据在ALRS进行的一次交叉孔试验中观察到的压力数据校准具有替代参数结构的气流模型，并检查它们以及MLBMA预测其他此类（验证）试验中观察到的压力的能力。将选择跨井测试，以便在每个井眼的不同井眼中进行注入。智力价值和广泛影响：提供最佳水文预测和预测不确定性评估的坚实理论和实用方法，这些不确定性共同考虑模型结构（概念数学框架）和参数的不确定性。该方法适用于广泛的模型，表示无处不在的开放和复杂的地球和环境系统中的自然过程。结果将通过各种方式广泛传播给研究人员和从业人员。