@article{Gómez-Déniz2026, 
author = {Emilio Gómez-Déniz and Nancy Dávila-Cárdenes and José María Pérez-Sánchez},
title = {A conjugate bivariate model suitable for detecting heterogeneity and getting evaluation marks via multiple-choice tests},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20170-20194},
keywords = {Bayesian, classroom, conjugate distribution, heterogeneity, loss function, marks, multiple-choice test},
url = {https://www.sciopen.com/article/10.3934/math.2026819},
doi = {10.3934/math.2026819},
abstract = {It is well known that academic performance varies in heterogeneous and homogeneous groups. In the latter, all students possess approximately the same level of instruction and skills. The results are usually measured by the marks achieved on exams. In this work, the marks calculated through this methodology could be considered a Bayes rule within the framework of statistical decision theory. With this methodology, we estimated the marks obtained on a multiple-choice test, considering individual student performance with the accumulated experience of the group. As a result, we addressed two major objectives: First, a mechanism was developed to detect the heterogeneity or homogeneity of the group based on the accumulated experience on past exams; and second, an evaluation system was proposed that rewarded or penalized students depending on their academic performance. The proposed framework may have implications for supporting students at risk, although such effects were not directly evaluated in this study.}
}