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Inference in two-piece location-scale models with Jeffreys Priors

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Rubio, Francisco J. and Steel, Mark F. J. (2014) Inference in two-piece location-scale models with Jeffreys Priors. Bayesian Analysis, 9 (1). pp. 1-21. doi:10.1214/13-BA849

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Official URL: http://dx.doi.org/10.1214/13-BA849

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Abstract

This paper addresses the use of Jeffreys priors in the context of univariate three-parameter location-scale models, where skewness is introduced by differing scale parameters either side of the location. We focus on various commonly used parameterizations for these models. Jeffreys priors are shown to lead to improper posteriors in the wide and practically relevant class of distributions obtained by skewing scale mixtures of normals. Easily checked conditions under which independence Jeffreys priors can be used for valid inference are derived. We also investigate two alternative priors, one of which is shown to lead to valid Bayesian inference for all practically interesting parameterizations of these models and is our recommendation to practitioners. We illustrate some of these models using real data.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Bayesian statistical decision theory
Journal or Publication Title: Bayesian Analysis
Publisher: International Society for Bayesian Analysis
ISSN: 1931-6690
Official Date: March 2014
Dates:
DateEvent
March 2014Published
24 February 2014Available
15 August 2013Available
Volume: 9
Number: 1
Page Range: pp. 1-21
DOI: 10.1214/13-BA849
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
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