Objective Bayesian Inference for the Half-Normal and Half-t Distributions

In this article, Bayesian inference for the half-normal and half-t distributions using uninformative priors is considered. It is shown that exact Bayesian inference can be undertaken for the half-normal distribution without the need for Gibbs sampling. Simulation is then used to compare the sampling properties of Bayesian point and interval estimators with those of their maximum likelihood based counterparts. Inference for the half-t distribution based on the use of Gibbs sampling is outlined, and an approach to model comparison based on the use of Bayes factors is discussed. The fitting of the half-normal and half-t models is illustrated using real data on the body fat measurements of elite athletes.

[1]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[2]  C. Robert.  Simulation of truncated normal variables , 2009, 0907.4010.

[3]  S. Walker,et al.  Sampling Truncated Normal, Beta, and Gamma Densities , 2001 .

[4]  J. Geweke,et al.  Bayesian Treatment of the Independent Student- t Linear Model , 1993 .

[5]  A. Azzalini,et al.  Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution , 2003, 0911.2342.

[6]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[7]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[8]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[9]  C. B. Morgan.  Truncated and Censored Samples, Theory and Applications , 1993 .

[10]  J. Berger,et al.  The Intrinsic Bayes Factor for Model Selection and Prediction , 1996 .

[11]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[12]  A. Pewsey.  LARGE-SAMPLE INFERENCE FOR THE GENERAL HALF-NORMAL DISTRIBUTION , 2002 .

[13]  Mathieu Kessler,et al.  On intrinsic priors for nonnested models , 2004 .

[14]  Arthur Pewsey.  Improved Likelihood Based Inference for the General Half-Normal Distribution , 2004 .

[15]  A. O'Hagan,et al.  Bayes estimation subject to uncertainty about parameter constraints , 1976 .

[16]  James O. Berger,et al.  An overview of robust Bayesian analysis , 1994 .

[17]  W. Meeusen,et al.  Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error , 1977 .

[18]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[19]  R. Elandt.  The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments , 1961 .

[20]  Andrea Tancredi.  Accounting for heavy tails in stochastic frontier models. , 2002 .

[21]  S. Chib,et al.  Marginal Likelihood From the Metropolis–Hastings Output , 2001 .

[22]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[23]  S. Wright,et al.  Genetics of Natural Populations. X. Dispersion Rates in Drosophila Pseudoobscura. , 1943, Genetics.

[24]  Adrian F. M. Smith,et al.  Bayesian Analysis of Constrained Parameter and Truncated Data Problems , 1991 .

[25]  David Ríos Insua,et al.  Robust Bayesian analysis , 2000 .

[26]  John Geweke,et al.  Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities , 1991 .

[27]  Brani Vidakovic,et al.  Efficiency of Linear Bayes Rules for a Normal Mean: Skewed Priors Class , 1995 .

[28]  Jurgen Haberle,et al.  Strength and failure mechanisms of unidirectional carbon fibre-reinforced plastics under axial compression , 1992 .

[29]  A. O'Hagan,et al.  Statistical Methods for Eliciting Probability Distributions , 2005 .

[30]  D. Aigner,et al.  P. Schmidt, 1977,?Formulation and estimation of stochastic frontier production function models,? , 1977 .

[31]  Skew-Elliptical Distributions in Bayesian Inference , 2004 .

[32]  George E. P. Box,et al.  Bayesian Inference in Statistical Analysis: Box/Bayesian , 1992 .

[33]  M. C. Jones,et al.  A skew extension of the t‐distribution, with applications , 2003 .