Abstract
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 postprocessing 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 the 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 characterization of the El Niño Southern Oscillation.
Highlights
Modern measuring equipment allows scientists and engineers to interrogate physical phenomena and behaviours that were royalsocietypublishing.org/journal/rsos R
The mean, μ, defines the peak value in the bell-shaped curve of the Gaussian distribution, while the random error or standard deviation, σ, characterizes the width of the curve; to inform decision-making, a 95% confidence interval can be defined as [measured value ± 2σ]. In those cases where no knowledge about the probabilistic form of the uncertainty exists, the error can be represented using interval analysis [26], in which the confidence interval is replaced with a range that represents the associated uncertainty, i.e. [measured value ± 2umeas], where umeas represents the measurement error, usually obtained from a calibration. This latter approach is recommended in the European Committee for Standardization (CEN) guide for the validation of computational solid mechanics models [27]
In various applications where decisions need to be made about whether two states are equivalent, for example, in condition monitoring or model validation, when the associated uncertainties are not negligible and the decision is to be based on a representation of the data in a lower dimensional form, it is important to be able to assess whether a pair of feature vectors belongs to the same population, and this assessment should be made by evaluating the difference in corresponding shape descriptors using the associated uncertainty for the shape descriptor
Summary
Modern measuring equipment allows scientists and engineers to interrogate physical phenomena and behaviours that were royalsocietypublishing.org/journal/rsos R.
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