# Credible Interval Prediction of a Nonstationary Poisson Distribution based on Bayes Decision Theory

### Daiki Koizumi

#### Abstract

A credible interval prediction problem of a nonstationary Poisson distribution in terms of Bayes decision theory is considered. This is the two-dimensional optimization problem of the Bayes risk function with respect to two variables: upper and lower limits of credible interval prediction. We prove that these limits can be uniquely obtained as the upper or lower percentile points of the predictive distribution under a certain loss function. By applying this approach, the Bayes optimal prediction algorithm for the credible interval is proposed. Using real web traffic data, the performance of the proposed algorithm is evaluated by comparison with the stationary Poisson distribution.

Download#### Paper Citation

#### in Harvard Style

Koizumi D. (2020). **Credible Interval Prediction of a Nonstationary Poisson Distribution based on Bayes Decision Theory**.In *Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-395-7, pages 995-1002. DOI: 10.5220/0009182209951002

#### in Bibtex Style

@conference{icaart20,

author={Daiki Koizumi},

title={Credible Interval Prediction of a Nonstationary Poisson Distribution based on Bayes Decision Theory},

booktitle={Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2020},

pages={995-1002},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009182209951002},

isbn={978-989-758-395-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - Credible Interval Prediction of a Nonstationary Poisson Distribution based on Bayes Decision Theory

SN - 978-989-758-395-7

AU - Koizumi D.

PY - 2020

SP - 995

EP - 1002

DO - 10.5220/0009182209951002