Objective Bayesian Analysis of Skew-t Distributions

Marcia D.Elia Branco; Marc G. Genton; Brunero Liseo

doi:10.1111/j.1467-9469.2011.00779.x

Objective Bayesian Analysis of Skew-t Distributions

Marcia D.Elia Branco, Marc G. Genton^*, Brunero Liseo

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student's t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew-t distributions.

Original language	English (US)
Pages (from-to)	63-85
Number of pages	23
Journal	Scandinavian Journal of Statistics
Volume	40
Issue number	1
DOIs	https://doi.org/10.1111/j.1467-9469.2011.00779.x
State	Published - Mar 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Branco's research was partially supported by FAPESP grant 04/15304-6. Genton's research was partially supported by NSF grant DMS-1007504. This publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). The authors thank the editor, an associate editor and a referee for their helpful comments and suggestions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Keywords

Approximation
Jeffreys prior
Maximum a posteriori estimator
Maximum likelihood estimator
Skew-normal
Skew-symmetric
Skew-t

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1111/j.1467-9469.2011.00779.x

Cite this

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title = "Objective Bayesian Analysis of Skew-t Distributions",

abstract = "We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student's t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew-t distributions.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Branco's research was partially supported by FAPESP grant 04/15304-6. Genton's research was partially supported by NSF grant DMS-1007504. This publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). The authors thank the editor, an associate editor and a referee for their helpful comments and suggestions. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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Objective Bayesian Analysis of Skew-t Distributions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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