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Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

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Gómez Villegas, Miguel A. and González Pérez, Beatriz (2013) Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test. Statistics: A Journal of Theoretical and Applied Statistics, 47 (3). pp. 558-565. ISSN 0233-1888

Official URL: http://www.tandfonline.com/doi/abs/10.1080/02331888.2012.658396#.UdFggDvwm4Q


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Abstract

A Bayesian test for H-0: = (0) versus H-1: (0) is developed. The methodology consists of fixing a sphere of radius around (0), assigning to H-0 a prior mass, (0), computed by integrating a density function () over this sphere, and spreading the remainder, 1(0), over H-1 according to (). The ultimate goal is to show when p values and posterior probabilities can give rise to the same decision in the following sense. For a fixed level of significance , when do (12) exist such that, regardless of the data, a Bayesian proponent who uses the proposed mixed prior with (0)((1), (2)) reaches, by comparing the posterior probability of H-0 with 1/2, the same conclusion as a frequentist who uses to quantify the p value? A theorem that provides the required constructions of (1) and (2) under verification of a sufficient condition ((12)) is proved. Some examples are revisited.


Item Type:Article
Uncontrolled Keywords:posterior probability; multivariate point null hypothesis; p-value; Lindley's paradox; 62F15; 62F03
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:22169
Deposited On:01 Jul 2013 11:01
Last Modified:04 Mar 2016 15:19

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