A simple analysis of the exact probability matching prior in the location-scale model

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Title: A simple analysis of the exact probability matching prior in the location-scale model
Author(s): DiCiccio, TJ
Kuffner, TA
Young, GA
Item Type: Journal Article
Abstract: It has long been asserted that in univariate location-scale models, when concerned with inference for either the location or scale parameter, the use of the inverse of the scale parameter as a Bayesian prior yields posterior credible sets which have exactly the correct frequentist confidence set interpretation. This claim dates to at least Peers (1965), and has subsequently been noted by various authors, with varying degrees of justification. We present a simple, direct demonstration of the exact matching property of the posterior credible sets derived under use of this prior in the univariate location-scale model. This is done by establishing an equivalence between the conditional frequentist and posterior densities of the pivotal quantities on which conditional frequentist inferences are based.
Publication Date: 29-Jun-2017
Date of Acceptance: 25-Oct-2016
URI: http://hdl.handle.net/10044/1/53480
DOI: https://dx.doi.org/10.1080/00031305.2016.1255662
ISSN: 1537-2731
Publisher: Taylor & Francis
Journal / Book Title: The American statistician
Copyright Statement: This is an Accepted Manuscript of an article published by Taylor & Francis Group in The American statisticianon 29 June 2017 available online at: http://www.tandfonline.com/10.1080/00031305.2016.1255662
Keywords: 0104 Statistics
Statistics & Probability
Publication Status: Published
Embargo Date: 2018-06-29
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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