Combining information from several experiments with nonparametric priors

SUMMARY This paper considers combining information from several experiments when the experiments can be summarised via a parameter value. The structure of this set of parameters, in terms of independence, exchangeability, partial exchangeability, etc., is assumed to be unknown and a finite number of possible structures are entertained, each with an associated prior weight representing the degree of belief in that structure. Crucial is the criterion by which these structures are selected. The final inference for the parameter values is taken to be the average, with respect to the posterior weights, of the values obtained from each structure. This is performed within a Bayesian nonparametric framework where the form of the prior distribution for the parameters is unrestricted. Therefore we do not assume that the distributions associated with a partial structure are from the same family. Different types of experiment suggest different types of distributions of parameters associated with each type of experiment.