, Volume 6, Issue 1, pp 205–221

Hierarchical models with scale mixtures of normal distributions

  • S. T. B. Choy
  • A. F. M. Smith

DOI: 10.1007/BF02564434

Cite this article as:
Choy, S.T.B. & Smith, A.F.M. Test (1997) 6: 205. doi:10.1007/BF02564434


In this paper, we consider the one-way random effects model as a Bayesian hierarchical structure, assuming normality for the first stage. We take scale mixtures of normal (SMN) distributions for the random effects in order to study the influential effects of aberrant random effects. For the sake of simplicity, conjugate priors are assigned to the hyperparameters. We show that the Gibbs sampler deals with this extension without any difficulties. The required random variate generation from the full conditionals of the mixing parameters of the SMN distributions is discussed at length. Potential outliers can be identified using these mixing parameters. More importantly, we show that the SMN distributions can protect inference from outliers and robustified analyses are therefore provided. Finally, we study the sensitivity of Bayes estimates of the population parameters to the choice of the second stage prior for the random effects.


Random Effects ModelsHierarchical ModelsGibbs SamplerRobustnessScale Mixture of NormalsStudentstStable FamilyPositive Stable Random VariableExponential-Power FamilyRatlo-of-UniformsAdaptive Rejection samplingSensitivity Analysis

Copyright information

© SEIO 1997

Authors and Affiliations

  • S. T. B. Choy
    • 1
  • A. F. M. Smith
    • 2
  1. 1.Department of StatisticsThe University of Hong KongHong Kong
  2. 2.Department of MathematicsImperial College LondonLondonU.K.