SUMMARY

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 approxi-mations for the Þrst and second moments of the parameters of a Bayesian random e¤ects model for meta-analysis. These computationally inexpensive methods are based on simple analytical formulae that provide an e¦cient 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. Statist. Med., 17, 201Ð218 (1998) 1