  In Bayesian meta-analysis, the specification of prior probabilities for the
between-study heterogeneity is commonly required, and is of particular benefit
in situations where only few studies are included. Among the considerations in
the set-up of such prior distributions, the consultation of available empirical
data on a set of relevant past analyses sometimes plays a role. How exactly to
summarize historical data sensibly is not immediately obvious; in particular,
the investigation of an empirical collection of heterogeneity estimates will
not target the actual problem and will usually only be of limited use. The
commonly used normal-normal hierarchical model for random-effects meta-analysis
is extended to infer a heterogeneity prior. Using an example data set, we
demonstrate how to fit a distribution to empirically observed heterogeneity
data from a set of meta-analyses. Considerations also include the choice of a
parametric distribution family. Here, we focus on simple and readily applicable
approaches to then translate these into (prior) probability distributions.
