ABSTRACT
The specification of priors for variance components may become more important in hierarchical models; particularly when more vague priors are desired. In fact, A. Gelman recommended against using vague inverse gamma priors for latent variance parameters in hierarchical models, and preferred instead half-Cauchy or uniform prior distributions for standard deviations. As with the normal prior for the mean parameter μ, the inverse gamma prior for the variance parameter σ2 is only one option. Many different approaches have been used to provide prior information for σ2, including log-normal, truncated normal, Cauchy, gamma, and inverse gamma. The inverse gamma prior for σ2 is conjugate but that does not mean that it is the most intuitive, nor does it have the best properties.
