## Bayesian Analysis

### Inference in Two-Piece Location-Scale Models with Jeffreys Priors

#### 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.

#### Article information

Source
Bayesian Anal., Volume 9, Number 1 (2014), 1-22.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1393251764

Digital Object Identifier
doi:10.1214/13-BA849

Mathematical Reviews number (MathSciNet)
MR3188293

Zentralblatt MATH identifier
1327.62157

#### Citation

Rubio, Francisco J.; Steel, Mark F. J. Inference in Two-Piece Location-Scale Models with Jeffreys Priors. Bayesian Anal. 9 (2014), no. 1, 1--22. doi:10.1214/13-BA849. https://projecteuclid.org/euclid.ba/1393251764

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#### See also

• Related item: José M. Bernardo. Comment on Article by Rubio and Steel. Bayesian Anal., Vol. 9, Iss. 1 (2014) 23–24.
• Related item: James G. Scott. Comment on Article by Rubio and Steel. Bayesian Anal., Vol. 9, Iss. 1 (2014) 25–28.
• Related item: Robert E. Weiss and Marc A. Suchard. Comment on Article by Rubio and Steel. Bayesian Anal., Vol. 9, Iss. 1 (2014) 29–38.
• Related item: Xinyi Xu. Comment on Article by Rubio and Steel. Bayesian Anal., Vol. 9, Iss. 1 (2014) 39–44.
• Related item: Francisco J. Rubio and Mark F. J. Steel. Rejoinder. Bayesian Anal., Vol. 9, Iss. 1 (2014) 45–52.