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Bayesian inference for the half-normal and half-t distributions

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  • Wiper, Michael Peter
  • Giron, F.J.
  • Pewsey, A.

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.

Suggested Citation

  • Wiper, Michael Peter & Giron, F.J. & Pewsey, A., 2005. "Bayesian inference for the half-normal and half-t distributions," DES - Working Papers. Statistics and Econometrics. WS ws054709, Universidad Carlos III de Madrid. Departamento de Estadística.
  • 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 19-40, 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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