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Bayesian Inference For The Half-Normal And Half-T Distributions

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  • Michael P. Wiper

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  • F.J. Giron
  • A. Pewsey
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    Abstract

    In this article we consider approaches to Bayesian inference for the half-normal and half-t distributions. We show that a generalized version of the normal-gamma distribution is conjugate to the half-normal likelihood and give the moments of this new distribution. The bias and coverage of the Bayesian posterior mean estimator of the halfnormal location parameter are compared with those of maximum likelihood based estimators. Inference for the half-t distribution is performed using Gibbs sampling and model comparison is carried out using Bayes factors. A real data example is presented which demonstrates the fitting of the half-normal and half-t models.

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    File URL: http://docubib.uc3m.es/WORKINGPAPERS/WS/ws054709.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws054709.

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    Date of creation: Jul 2005
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    Handle: RePEc:cte:wsrepe:ws054709

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    1. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
    2. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    3. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
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