# On the Prediction of a Nonstationary Bernoulli Distribution based on Bayes Decision Theory

### Daiki Koizumi

#### Abstract

A class of nonstationary Bernoulli distribution is considered in terms of Bayes decision theory. In this nonstationary class, the Bernoulli distribution parameter follows a random walking rule. Even if this general class is assumed, it is proved that the posterior distribution of the parameter can be obtained analytically with a known hyper parameter. With this theorem, the Bayes optimal prediction algorithm is proposed assuming the 0-1 loss function. Using real binary data, the predictive performance of the proposed model is evaluated comparing to that of a stationary Bernoulli model.

Download#### Paper Citation

#### in Harvard Style

Koizumi D. (2021). **On the Prediction of a Nonstationary Bernoulli Distribution based on Bayes Decision Theory**.In *Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-484-8, pages 957-965. DOI: 10.5220/0010270709570965

#### in Bibtex Style

@conference{icaart21,

author={Daiki Koizumi},

title={On the Prediction of a Nonstationary Bernoulli Distribution based on Bayes Decision Theory},

booktitle={Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2021},

pages={957-965},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010270709570965},

isbn={978-989-758-484-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - On the Prediction of a Nonstationary Bernoulli Distribution based on Bayes Decision Theory

SN - 978-989-758-484-8

AU - Koizumi D.

PY - 2021

SP - 957

EP - 965

DO - 10.5220/0010270709570965