On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

• 作者: Nengak Emmanuel Goltong Sani Ibrahim Doguwa
• 来源期刊: 统计学期刊(英文)
• 学科: 医学
• 关键词: Behrens-Fisher PROBLEM Lindley's PARADOX METROPOLIS-HASTINGS Algorithm PARETO Prior t Distribution
• 年，卷（期）: 2019,（1）
• 页码范围: 1-14
• 页数: 14页
• 分类号: R73

摘要

In this paper we have demonstrated the ability of the new Bayesian measure of evidence of Yin (2012, Computational Statistics, 27: 237-249) to solve both the Behrens-Fisher problem and Lindley's paradox. We have provided a general proof that for any prior which yields a linear combination of two independent t random variables as posterior distribution of the di erence of means, the new Bayesian measure of evidence given that prior will solve Lindleys' paradox thereby serving as a general proof for the works of Yin and Li (2014, Journal of Applied Mathematics, 2014(978691)) and Goltong?and Doguwa (2018, Open Journal of Statistics, 8: 902-914).?Using the Pareto prior as an example, we have shown by the use of?simulation results that the new Bayesian measure of evidence solves?Lindley's paradox.