Approximate Bayesian inference for random effects meta-analysis

Whilst meta‐analysis is becoming a more commonplace statistical technique, Bayesian inference in meta‐analysis requires complex computational techniques to be routinely applied. We consider simple approximations for the first and second moments of the parameters of a Bayesian random effects model for meta‐analysis. These computationally inexpensive methods are based on simple analytical formulae that provide an efficient tool for a qualitative analysis and a quick numerical estimation of posterior quantities. They are shown to lead to sensible approximations in two examples of meta‐analyses and to be in broad agreement with the more computationally intensive Gibbs sampling. © 1998 John Wiley & Sons, Ltd.