Robust Bayesian analysis given priors on partition sets

In a Bayesian analysis, suppose that probability measures may be specified over the subsets partitioning the parameter space ?, in such a way that they can be combined to form a unique prior measure, defined over all ?, according to some weights. Should the weights be uncertain, then the class G{cyrillic} of all the probability measures compatible with such uncertainty is specified instead. Situations in which such a class G{cyrillic} is justified are presented and, in these cases, established and quite recent techniques in the field of robust Bayesian analysis are applied to G{cyrillic}. Bounds on posterior expectations are computed, as the prior measure varies in G{cyrillic}, whilst concentration functions and coefficients of divergence are considered when interest lies with comparing functional forms of measures in G{cyrillic}. © 1994 SEIO.