Conservative prior distributions for variance parameters in hierarchical models

Paul Gustafson, Shahadut Hossain, Ying C. Macnab

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Bayesian hierarchical models typically involve specifying prior distributions for one or more variance components. This is rather removed from the observed data, so specification based on expert knowledge can be difficult. While there are suggestions for "default" priors in the literature, often a conditionally conjugate inverse-gamma specification is used, despite documented drawbacks of this choice. The authors suggest " conservative" prior distributions for variance components, which deliberately give more weight to smaller values. These are appropriate for investigators who are skeptical about the presence of variability in the second-stage parameters (random effects) and want to particularly guard against inferring more structure than is really present. The suggested priors readily adapt to various hierarchical modelling settings, such as fitting smooth curves, modelling spatial variation and combining data from multiple sites.

Original languageEnglish
Pages (from-to)377-390
Number of pages14
JournalCanadian Journal of Statistics
Issue number3
Publication statusPublished - Sept 2006
Externally publishedYes


  • Bayesian analysis
  • Hierarchical model
  • Linear mixed model
  • Prior distribution
  • Variance component

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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