Bayesian estimation and regularization techniques in categorical data analysis

J. Kalina

doi:10.2478/jamsi-2025-0011

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Bayesian estimation and regularization techniques in categorical data analysis

Journal of Applied Mathematics, Statistics and Informatics

Volume 21 (2025): Issue 2 (December 2025)

By: J. Kalina

Open Access

|Dec 2025

Abstract

This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting Bayesian estimators for the binomial distribution and investigating their properties. Next, we develop hypothesis tests for categorical data (sign test, homogeneity test, symmetry test) based on regularized maximum likelihood estimates of the probabilities. Finally, we formulate regularized versions of common association measures for contingency tables and study the regularized version of mutual information, particular for the situation where the regularized version can effectively handle zero counts.

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Articles in this issue

DOI: https://doi.org/10.2478/jamsi-2025-0011 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180

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Language: English

Page range: 105 - 122

Published on: Dec 26, 2025

Published by: University of Ss. Cyril and Methodius in Trnava

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

contingency tables,

mutual information,

zero-count adjustment,

homogeneity test,

symmetry test

Related subjects:

Computer sciences,

Information technology,

Mathematics,

Logic and set theory,

Probability and statistics,

Applied mathematics

© 2025 J. Kalina, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 21 (2025): Issue 2 (December 2025)