Thresholdsbetween

Thresholdsbetween is a term used in statistics and machine learning to describe the collection of threshold values that lie between two adjacent decision boundaries in a scoring or classification system. In many models, scores are converted into discrete decisions by applying one or more thresholds. The open intervals between these thresholds define thresholdsbetween, a concept used for sensitivity analysis, calibration, and robust decision making.

Formally, let s(x) be a scoring function taking real values and let t1 < t2 < ... < tk be consecutive decision thresholds that map score ranges to categories. Thresholdsbetween is the union of the open intervals (ti, t_{i+1}) for i = 1, ..., k-1. Exploring thresholdsbetween involves examining how small calibrations within such an interval affect outputs, metrics, or risk classifications without crossing a primary boundary.

Applications include medical risk scoring, credit risk grading, and image or signal classification where multiple risk or priority bins are defined. An analyst may vary a threshold t within a given gap to study calibration or to determine the stability of decisions against threshold drift. This is related to, but distinct from, standard threshold analysis which focuses on a single tipping point.

Limitations and notes: thresholdsbetween is a descriptive concept rather than a universal statistical object; its practical meaning depends on how thresholds are used to partition scores into categories. Care is needed to ensure that analyses of thresholdsbetween do not imply changes in the underlying model performance unless the category assignments actually change.

See also: threshold, decision boundary, calibration, score distribution, ROC curve, precision-recall.