An Objective Bayesian Analysis of the Powered Ratio of Multinomial Proportions

• 발행기관: 한국자료분석학회
• 저자명: Ju-Sung Kim Hea-Jung Kim Kang-Jin Hwang
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.15 No.3, 1171~1181쪽, 전체 11쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2013.06.30

영문 초록

This paper proposes a probability matching prior for performing objective Bayesian analysis of a powered ratio of multinomial proportions. The prior is derived by using the Tibshirani’s method that facilitates an orthogonal parameterization. Two numerical illustrations demonstrate that the proposed prior has good probability matching property with respect to the frequentist coverage probability. The illustrations also show the better performance of the prior over the Jeffreys prior in terms of the coverage probability and the accuracy in posterior estimation of the ratio. A Markov chain Monte Carlo method that facilitates the Metropolis-Hastings algorithm is considered to implement posterior analysis of the powered ratio. It is shown that the computational method is straightforward to specify distribution and to implement computation whose output is readily adapted for required posterior summaries.

목차

1. Introduction

2. Tibshirani’s Probability Matching Prior

3. Posterior Analysis

4. Numerical Illustrations

5. Concluding Remarks

References

키워드

multinomial proportions powered ratio probability matching prior objective Bayesian analysis