COMBINING INFORMATION FROM SEVERAL EXPERIMENTS WITH NONPARAMETRIC PRIORS

This paper considers combining information from several experiments wh en the experiments can be summarised via a parameter value. The struct ure of this set of parameters, in terms of independence, exchangeabili ty, partial exchangeability, etc., is assumed to be unknown and a fini te number of possible structures are entertained, each with an associa ted prior weight representing the degree of belief in that structure. Crucial is the criterion by which these structures are selected. The f inal inference for the parameter values is taken to be the average, wi th 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 unrest ricted. Therefore we do not assume that the distributions associated w ith a partial structure are from the same family. Different types of e xperiment suggest different types of distributions of parameters assoc iated with each type of experiment.