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.