GNOSTICS

Mathematical Gnostics is a non-statistical tool used to efficiently treat small samples of strongly uncertain data. It consists of... The axiomatic theory of uncertainty of individual uncertain data and small data samples,... Gnostic data weight and irrelevance manifest their natural robustness of two kinds: the estimating characteristics are robust with respect to outliers (peripheral data) while the quantifying ones are robust to inliers (to central data and noises) of the data sample). This feature makes them suitable to be applied to strongly uncertain data. However, it can be shown, that all these characteristics converge to statistical ones when the uncertainty is very weak: data irrelevances converge to ordinary (Euclidean) errors and the data weights converge to squared errors. This presents the classical (non-robust) statistics as a tool for handling "relatively good" data and Gnostics as its robust extension having its own, different theoretical fundament justifying its..