  The normal-normal hierarchical model (NNHM) constitutes a simple and widely
used framework for meta-analysis. In the common case of only few studies
contributing to the meta-analysis, standard approaches to inference tend to
perform poorly, and Bayesian meta-analysis has been suggested as a potential
solution. The Bayesian approach, however, requires the sensible specification
of prior distributions. While non-informative priors are commonly used for the
overall mean effect, the use of weakly informative priors has been suggested
for the heterogeneity parameter, in particular in the setting of (very) few
studies. To date, however, a consensus on how to generally specify a weakly
informative heterogeneity prior is lacking. Here we investigate the problem
more closely and provide some guidance on prior specification.
