The Gini–Bayes Connection: The CAP Slope as Bayes' Theorem, with Applications to Weight of Evidence, Somers' D, and Calibration

Battle Count: 55

The paper is firmly in credit risk and scorecard methodology, not quantitative trading. However, the Gini/AUC/Somers' D identity and calibration diagnostics are transferable to any binary classification context including trading signal evaluation. The weight of evidence framework could inform factor model interpretation. Direct relevance to trading strategy development is minimal.

The core identity (CAP slope = Bayes' theorem in cumulative coordinates) is a one-line derivation. Computing the accuracy ratio three ways, WOE, IV, and comparison-mode CAPs are straightforward discrete operations. The continuous KDE example requires density estimation but is well-supported by SciPy. No complex optimization or training is involved.

All numbers, tables, and figures are reproduced by code at https://github.com/deburky/gini-bayes-paper using numpy and SciPy. The five-band discrete example and continuous KDE example are fully scripted. Exact rational values are used for the discrete case.