## Brazilian Journal of Probability and Statistics

### Bayesian analysis of multiple-inflation Poisson models and its application to infection data

#### Abstract

In this article we propose a multiple-inflation Poisson regression to model count response data containing excessive frequencies at more than one non-negative integer values. To handle multiple excessive count responses, we generalize the zero-inflated Poisson regression by replacing its binary regression with the multinomial regression, while Su et al. [Statist. Sinica 23 (2013) 1071–1090] proposed a multiple-inflation Poisson model for consecutive count responses with excessive frequencies. We give several properties of our proposed model, and do statistical inference under the fully Bayesian framework. We perform simulation studies and also analyze the data related to the number of infections collected in five major hospitals in Turkey, using our methodology.

#### Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 2 (2018), 239-261.

Dates
Accepted: October 2016
First available in Project Euclid: 17 April 2018

https://projecteuclid.org/euclid.bjps/1523952014

Digital Object Identifier
doi:10.1214/16-BJPS340

Mathematical Reviews number (MathSciNet)
MR3787753

Zentralblatt MATH identifier
06914674

#### Citation

Ryu, Duchwan; Bilgili, Devrim; Ergönül, Önder; Ebrahimi, Nader. Bayesian analysis of multiple-inflation Poisson models and its application to infection data. Braz. J. Probab. Stat. 32 (2018), no. 2, 239--261. doi:10.1214/16-BJPS340. https://projecteuclid.org/euclid.bjps/1523952014

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