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Bayesian modelling with skew-elliptical distributions

Bayesian modelling with skew-elliptical distributions
Bayesian modelling with skew-elliptical distributions

The dissertation is devoted to modelling with a new class of multivariate skew elliptical distributions.  This family of distributions extends the elliptical ones by the addition of a vector of shape parameters.  It contains the multivariate skew normal, skew Student’s t and skew Cauchy as special cases.

Detailed exploration is confined to the case of the univariate skew normal distribution.  In particular, salient properties of the density are studied and comparisons are drawn with alternative skew normal proposals.  Applications considered include linear regression, variance components and survival models.  Bayesian analysis with these models are shown to be easily accomplished through the use of the Gibbs sampler.  The latter proves very straightforward to specify distributionally and to implement computationally.  Numerical examples show that skew normal modelling is a viable competitor to the celebrated normal theory methods.

University of Southampton
Chai, High Seng
3cc1c0af-eb45-40ee-bef8-07b7a4494ee7
Chai, High Seng
3cc1c0af-eb45-40ee-bef8-07b7a4494ee7

Chai, High Seng (2004) Bayesian modelling with skew-elliptical distributions. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The dissertation is devoted to modelling with a new class of multivariate skew elliptical distributions.  This family of distributions extends the elliptical ones by the addition of a vector of shape parameters.  It contains the multivariate skew normal, skew Student’s t and skew Cauchy as special cases.

Detailed exploration is confined to the case of the univariate skew normal distribution.  In particular, salient properties of the density are studied and comparisons are drawn with alternative skew normal proposals.  Applications considered include linear regression, variance components and survival models.  Bayesian analysis with these models are shown to be easily accomplished through the use of the Gibbs sampler.  The latter proves very straightforward to specify distributionally and to implement computationally.  Numerical examples show that skew normal modelling is a viable competitor to the celebrated normal theory methods.

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Published date: 2004

Identifiers

Local EPrints ID: 466025
URI: http://eprints.soton.ac.uk/id/eprint/466025
PURE UUID: f56bb577-5502-4888-9318-e727c65fba0a

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Date deposited: 05 Jul 2022 04:01
Last modified: 16 Mar 2024 20:28

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Author: High Seng Chai

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