Manuscript received April 1, 2026; accepted June 3, 2026; published July 14, 2026
Abstract—When classes are imbalanced, the evaluation of binary classification algorithms presents a structural problem: the prevalence of the positive class varies widely across practical applications, from fraud detection and system monitoring to disease identification in medical and epidemiological settings. In these scenarios, classical accuracy yields misleadingly high values that fail to capture true discriminative capacity, as it is operates as a linear function of prevalence, dominated by the majority class and unable to penalize the trivial classifier that labels everything as the dominant class. To address this limitation, Bayesian Geometric Accuracy, defined as the geometric mean of the positive and negative predictive values, is proposed. Unlike classical accuracy, this metric is nonlinear in prevalence, vanishes at both extremes, and penalizes class imbalance by construction because predictive values explicitly depend on prevalence through Bayes' theorem. The equivalence condition between both measures yields a degree 3 polynomial in prevalence, whose coefficients are expressed in closed form in terms of sensitivity, specificity, and the Youden index. This polynomial has exactly two roots in the unit interval, and their separation constitutes a principled measure of the classifier's discriminative strength. The framework is illustrated through a multilayer perceptron trained on spectral indices for the binary classification of disease presence in potato crops, where classical accuracy is 0.868 while Bayesian Geometric Accuracy yields 0.655, a gap that reveals a substantial overestimation at the observed prevalence of 12.7%. The proposed metric defines a principled safe interval of class ratios that may guide a more robust model design for detecting early crop disease.
Keywords—Bayesian accuracy, positive predictive value, negative predictive value, class imbalance
Cite: Aquiles Darghan, Ivan Lizarazo, Carlos Rivera, Liliana Castillo-Villamor, and Jorge Jola, "Beyond Accuracy: A Bayesian Metric for Binary Classifier Evaluation in Imbalanced Crop Disease Data," International Journal of Machine Learning vol. 16, no. 2, pp. 7-16, 2026.
Copyright © 2026 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).