On the Prediction of a Nonstationary Geometric Distribution Based on Bayes Decision Theory

Daiki Koizumi

2025

Abstract

This paper considers a prediction problem with a nonstationary geometric distribution in terms of Bayes decision theory. The proposed nonstationary statistical model contains a single hyperparameter, which is used to express the nonstationarity of the parameter of the geometric distribution. Furthermore, the proposed predictive algorithm is based on both the posterior distribution of the nonstationary parameter and the predictive distribution for data, operating with a Bayesian context. Each predictive estimator satisfies the Bayes optimality, which guarantees a minimum mean error rate with the proposed nonstationary probability model, a loss function, and a prior distribution of the parameter in terms of Bayes decision theory. Furthermore, an approximate maximum likelihood estimation method for the hyperparameter based on numerical calculation has been considered. Finally, the predictive performance of the proposed algorithm has been evaluated in terms of both the model selection theory and the predictive mean squared error by comparison with the stationary geometric distribution using real web traffic data.

Paper Citation

in Harvard Style

Koizumi D. (2025). On the Prediction of a Nonstationary Geometric Distribution Based on Bayes Decision Theory. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART; ISBN 978-989-758-737-5, SciTePress, pages 140-149. DOI: 10.5220/0013097500003890

in Bibtex Style

@conference{icaart25,
author={Daiki Koizumi},
title={On the Prediction of a Nonstationary Geometric Distribution Based on Bayes Decision Theory},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART},
year={2025},
pages={140-149},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013097500003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART
TI - On the Prediction of a Nonstationary Geometric Distribution Based on Bayes Decision Theory
SN - 978-989-758-737-5
AU - Koizumi D.
PY - 2025
SP - 140
EP - 149
DO - 10.5220/0013097500003890
PB - SciTePress