Conservative prior distributions for variance parameters in hierarchical models

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.