定量模型验证技术：新的见解
Quantitative model validation techniques: new insights
摘要：
本文发展了新的见解，定量方法的计算模型预测的验证。四种类型的方法进行了研究，即经典和贝叶斯假设检验，可靠性为基础的方法，和面积度量为基础的方法。传统的贝叶斯假设检验是基于分布参数的区间假设和概率分布的相等假设进行扩展的，以验证给定输入下具有确定性/随机性输出的模型。考虑两种类型的验证实验-完全表征（所有模型/实验输入均测量并报告为点值）和部分表征（一些模型/实验输入未测量或报告为区间）。贝叶斯假设检验可以通过合理选择模型接受阈值来降低模型选择的风险，其结果可以用于模型平均以避免I/II类错误。结果表明，贝叶斯区间假设检验，可靠性为基础的方法，和面积度量为基础的方法可以占方向性偏差的存在，其中数值模型的平均预测可能始终低于或高于相应的实验观察。研究还发现，在一定条件下，贝叶斯等式假设检验中的贝叶斯因子度量和基于可靠性的度量都可以与经典假设检验中的p值度量在数学上建立联系。将上述验证方法应用于射频（RF）微机电系统（MEMS）开关的气体阻尼预测，进行了数值研究。感兴趣的模型是一个通用的多项式混沌（gPC）代理模型构建的基础上昂贵的运行的基于物理的仿真模型，并从充分表征的实验收集验证数据。
英文摘要：
This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an area metric-based method. Traditional Bayesian hypothesis testing is extended based on interval hypotheses on distribution parameters and equality hypotheses on probability distributions, in order to validate models with deterministic/stochastic output for given inputs. Two types of validation experiments are considered - fully characterized (all the model/experimental inputs are measured and reported as point values) and partially characterized (some of the model/experimental inputs are not measured or are reported as intervals). Bayesian hypothesis testing can minimize the risk in model selection by properly choosing the model acceptance threshold, and its results can be used in model averaging to avoid Type I/II errors. It is shown that Bayesian interval hypothesis testing, the reliability-based method, and the area metric-based method can account for the existence of directional bias, where the mean predictions of a numerical model may be consistently below or above the corresponding experimental observations. It is also found that under some specific conditions, the Bayes factor metric in Bayesian equality hypothesis testing and the reliability-based metric can both be mathematically related to the p-value metric in classical hypothesis testing. Numerical studies are conducted to apply the above validation methods to gas damping prediction for radio frequency (RF) microelectromechanical system (MEMS) switches. The model of interest is a general polynomial chaos (gPC) surrogate model constructed based on expensive runs of a physics-based simulation model, and validation data are collected from fully characterized experiments.
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