Intrinsic priors for comparing zero-inflation parameters in Poisson models

Year 2025, Early Access, 1 - 17

Hyeon Jun Jeong Kipum Kim Yongdai Kim Seong Kim

https://doi.org/10.15672/hujms.1292359

Abstract

Prior elicitation is an important issue in both objective and subjective Bayesian inferences. In hypothesis testing and model selection, choosing appropriate prior distributions becomes significantly more critical. In an objective Bayesian analysis, one utilizes noninformative priors such as Jeffreys priors or reference priors for hypothesis testing which are often improper, making unspecified constants to be contained in the Bayes factor. Thus, the resulting Bayes factor should be adjusted. In this paper, we consider default Bayes procedures for testing zero-inflation parameters in a zero-inflated Poisson distribution. In particular, we derive a set of intrinsic priors based on an approximation procedure. Extensive simulations and analyses of two real datasets are performed to support the methodology developed in the paper. It is shown that the proposed Bayesian and frequentist approaches yield similar comparable results.

Keywords

Fractional Bayes factor, intrinsic Bayes factor, intrinsic prior, training sample

Supporting Institution

National Research Foundation of Korea

Project Number

NRF-2021R1A2C1005271; NRF-2020R1A2C3A01003550

Thanks

Y. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C3A01003550). S. W. Kim’s research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1A2C1005271).

References

• [1] I. A. Almodo´var-Rivera and L. R. Pericchi-Guerra, An objective and robust Bayes factor for the hypothesis test one sample and two population means, Entropy 26 (1), 1-25, 2024.