Robust Bayesian Analysis given Priors on Partitions Sets

In a Bayesian analysis, suppose that probability measures may be specified over the subsets partitioning the parameter space Ω, in such a way that they can be combined to form a unique prior measure, defined over all Ω, according to some weights. Should the weights be uncertain, then the class Г of all the probability measures compatible with such uncertainty is specified instead. Situations in which such a class Г is justified are presented and, in these cases, established and quite recent techniques in the field of robust Bayesian analysis are applied to Г. Bounds on posterior expectations are computed, as the prior measure varies in Г, whilst concentration functions and coefficients of divergence are considered when interest lies with comparing functional forms of measures in Г.