The Bayesian operating characteristic curve for feature analysis applied to urban land cover change

Abstract

The Total Operating Characteristic curve (TOC) is a visual tool used to assess the performance of binary classifiers, introduced as an improvement over the Receiver Operating Characteristic (ROC) curve. The TOC provides a function that maps the number of hits plus false alarms (True Positives and False Positives) to hits (True Positives). Despite its broad adoption in model evaluation, especially for land use change studies, the TOC’s mathematical properties for explaining the probabilistic performance of classifiers and data distributions remain underexplored. To fill this gap, this article introduces the Bayesian Operating Characteristic (BOC) curve, a novel explanatory framework derived from the application of Bayes’ theorem and numerical analysis on the TOC curve. Such a framework establishes the computation of cumulative and density distribution functions that describe and identify non-linear relations between a rank variable and its binary outcome, specifying the rank’s interval with the maximal positive or negative impact in the classification. The proposal is validated by the analysis and identification of urban land change drivers, revealing different non-linear probabilistic relationships between rank variables and the binary outcome.