On one-sample Bayesian tests for the mean. Issue 2 (3rd March 2020)

• Record Type: Journal Article
• Authors: Abdelrazeq, Ibrahim; Al-Labadi, Luai; Alzaatreh, Ayman
• Is Part Of: Statistics. Volume 54:Issue 2(2020)
• Page Start: 424
• Page End: 440
• Publication Date: 2020-03-03
• Subjects: Hypothesis testing -- Kullbak–Leibler divergence -- one-sample t-test -- one-sample z-test -- relative belief inferences; 62F03 -- 62F15; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1726918
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: This paper deals with a new Bayesian approach to the standard one-sample z - and t - tests. More specifically, let x 1, …, x n be an independent random sample from a normal distribution with mean μ and variance σ 2 . The goal is to test the null hypothesis H 0 : μ = μ 1 against all possible alternatives. The approach is based on using the well-known formula of the Kullbak–Leibler divergence between two normal distributions (sampling and hypothesized distributions selected in an appropriate way). The change of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Eliciting the prior, checking for prior-data conflict and bias are also considered. Many theoretical properties of the procedure have been developed. Besides it's simplicity, and unlike the classical approach, the new approach possesses attractive and distinctive features such as giving evidence in favour of the null hypothesis. It also avoids several undesirable paradoxes, such as Lindley's paradox that may be encountered by some existing Bayesian methods. The use of the approach has been illustrated through several examples.