The Concept of Exchangeability and its Applications

The general concept of exchangeability allows the more flexible modelling of most experimental setups. The representation theorems for exchangeable sequences of random variables establish that any coherent analysis of the information thus modelled requires the specification of a joint probability distribution on all the parameters involved, hence forcing a Bayesian approach. The concept of partial exchangeability provides a further refinement, by permitting appropriate modelling of related experimental setups, leading to coherent information integration by means of so-called hierarchical models. Recent applications of hierarchical models for combining information from similar experiments in education, medicine and psychology have been produced under the name of meta-analysis.

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