Nonparametric prior elicitation for a binomial proportion

Abstract

This paper proposes a nonparametric Bayesian approach based on a density estimation with an open unit interval (0,1) using binomial data. We propose a very efficient nonparametric Bayesian approach method to infer smooth density defined on (0,1) through the transformation of a random variable. For practical implementation, we provide the corresponding blocked Gibbs sampling procedure based on the stick-breaking representation. The greatest advantage of this method is that it does not require us to draw from the complete conditional posterior distribution using a Metropolis-Hastings transition probability because the proposed transformation leads to a pair of conjugate priors and likelihoods. The validity of the proposed method is assessed through simulated and real data analysis.

Keywords:

• Binomial proportion
• Blocked Gibbs sampling
• Dirichlet process mixture
• Nonparametric prior

Additional information

Funding

The research of Jung In Seo was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT & Future Planning) (No. 2017R1C1B1006792). The research of Yongku Kim was supported by by Basic Science Research Program through the Na- tional Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2018R1D1A1B07043352).