Data from: Transformation of measurement uncertainties into low-dimensional feature vector space

Advances in technology allow the acquisition of data with high spatial and
temporal resolution.  These datasets are usually accompanied by
estimates of the measurement uncertainty, which may be spatially or
temporally varying and should be taken into consideration when making
decisions based on the data.  At the same time, various
transformations are commonly implemented to reduce the dimensionality of
the datasets for post-processing, or to extract significant features.
However, the corresponding uncertainty is not usually represented in the
low-dimensional or feature vector space.  A method is proposed
that maps the measurement uncertainty into the equivalent low-dimensional
space with the aid of approximate Bayesian computation, resulting in a
distribution that can be used to make statistical inferences. The method
involves no assumptions about the probability distribution of the
measurement error and is independent of the feature extraction process as
demonstrated in three examples. In the first two examples Chebyshev
polynomials were used to analyse structural displacements and soil
moisture measurements; while in the third, principal component analysis
was used to decompose global ocean temperature data. The uses of the
method range from supporting decision making in model validation or
confirmation, model updating or calibration and tracking changes in
condition, such as the characterisation of the El Niño Southern
Oscillation.

技术进步使得获取兼具高空间分辨率与高时间分辨率的数据成为可能。此类数据集通常附带测量不确定度估计值，该不确定度可随空间或时间动态变化，在基于该数据开展决策时需将其纳入考量范畴。与此同时，为完成后处理或提取关键特征，学界通常会对数据集执行各类降维变换操作。然而，对应的测量不确定度通常并未在低维空间或特征向量空间中得到有效表征。本研究提出一种方法，借助近似贝叶斯计算（approximate Bayesian computation）将测量不确定度映射至等效低维空间，最终得到可用于统计推断的概率分布。该方法无需对测量误差的概率分布作出预设假设，且独立于特征提取流程，这一点已通过三个示例得到验证。在前两个示例中，研究采用切比雪夫多项式（Chebyshev polynomials）分别分析结构位移与土壤湿度测量数据；第三个示例则采用主成分分析（principal component analysis）对全球海洋温度数据进行分解。该方法的应用场景覆盖模型验证与确认、模型更新或校准，以及工况变化追踪（如厄尔尼诺-南方涛动（El Niño Southern Oscillation）的特征表征）等多个领域。