Bayesian Statistics
Working Paper 05-47 Statistics and Econometrics Series 09 July 2005
Departamento de Estadística Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624-98-49
BAYESIAN INFERENCE FOR THE HALF-NORMAL AND HALF-T DISTRIBUTIONS
M.P. Wiper, F.J. Girón, A. Pewsey*
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.
Keywords: Bias-correction; Gaussian-modulated gamma distribution; Gibbs sampling; likelihood based inference; model selection; right-truncated normal- gamma distribution.
* Wiper, Departamento de Estadística, Universidad Carlos III de Madrid, C/ Madrid 126, 28903 Getafe (Madrid ), e-mail: mwiper@est-econ.uc3m.es; Girón, Departamento de Estadística e Investigación Operativa, Universidad de Malaga; Pewsey, Departamento de Matemáticas, Universidad de Extremadura Departamento de Matemáticas, Universidad de Extremadura.
Bayesian inference for the half-normal and half-t distributions
M.P. Wiper∗ F.J. Gir´n† & A. Pewsey‡ , o , July 21, 2005
Abstract In this article we consider approaches to Bayesian inference for the halfnormal 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 half-normal location parameter
Departamento de Estadística Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624-98-49
BAYESIAN INFERENCE FOR THE HALF-NORMAL AND HALF-T DISTRIBUTIONS
M.P. Wiper, F.J. Girón, A. Pewsey*
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.
Keywords: Bias-correction; Gaussian-modulated gamma distribution; Gibbs sampling; likelihood based inference; model selection; right-truncated normal- gamma distribution.
* Wiper, Departamento de Estadística, Universidad Carlos III de Madrid, C/ Madrid 126, 28903 Getafe (Madrid ), e-mail: mwiper@est-econ.uc3m.es; Girón, Departamento de Estadística e Investigación Operativa, Universidad de Malaga; Pewsey, Departamento de Matemáticas, Universidad de Extremadura Departamento de Matemáticas, Universidad de Extremadura.
Bayesian inference for the half-normal and half-t distributions
M.P. Wiper∗ F.J. Gir´n† & A. Pewsey‡ , o , July 21, 2005
Abstract In this article we consider approaches to Bayesian inference for the halfnormal 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 half-normal location parameter