This paper develops inference and statistical decision for set-identi…ed parameters from the robust Bayes perspective. When a model is not identi…ed, prior knowledge for model parameters is decomposed into two components: the one that can be updated by data (revisable prior knowledge) and the one that never be updated (unrevisable prior knowledge). We accept a single prior distribution for the revisable and apply Bayesian updating, while we introduce the unconstrained class of prior distributions for the unrevisable, and develop an inference procedure that is free from the unrevisable prior knowledge. We summarize posterior uncertainty of the set-identi…ed parameters by the posterior lower and upper probabilities (Dempster (1967, 1968)). We develop point estimation of the set-identi…ed parameters based on the posterior gamma-minimax criterion, which is, in our context, equivalent to minimizing the Choquet expected loss with respect to the posterior upper probability. We also propose a use of the posterior lower probability to construct a posterior credible region for the set-identi…ed parameters. Our