量化模型在概率测度空间中的不确定性
Quantifying Model Uncertainties in the Space of Probability Measures
摘要：
由于缺乏科学的认识，在科学和工程中的复杂现象的数学建模中可能会缺少一些机制。因此，这些数学模型包含一些不确定性，例如不确定参数。估计这些参数的一种方法是基于路径观测，即，量化系统演化的样本路径空间中的模型不确定性。另一种方法是设计在这里估计不确定的参数，或未知的系统功能，根据实验观察系统演化的概率分布。这被称为在概率测度空间中模型不确定性的量化。几个例子来证明这种方法，解析或数值。
英文摘要：
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One method to estimate these parameters is based on pathwise observations, i.e., quantifying model uncertainty in the space of sample paths for system evolution. Another method is devised here to estimate uncertain parameters, or unknown system functions, based on experimental observations of probability distributions for system evolution. This is called the quantification of model uncertainties in the space of probability measures. A few examples are presented to demonstrate this method, analytically or numerically.
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