This chapter introduces a Bayesian approach to meta-analysis. It discusses the ways in which a Bayesian approach differs from the method of moments and maximum likelihood methods described in chapters 9 and 10, and summarizes the steps required for a Bayesian analysis. It shows that Bayesian methods provide the basis for a rich variety of very flexible models, explicit statements about uncertainty of model parameters, inclusion of other information relevant to an analysis, and direct probabilistic statements about parameters of interest. In a meta-analysis context, this allows for more straightforward accommodation of study-specific differences and similarities, nonnormality and other distributional features of the data, missing data, small studies, and so forth.
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