  Bayesian methods are useful for statistical inference. However, real-world
problems can be challenging using Bayesian methods when the data analyst has
only limited prior knowledge. In this paper we consider a class of problems,
called Partial Bayes problems, in which the prior information is only partially
available. Taking the recently proposed Inferential Model approach, we develop
a general inference framework for Partial Bayes problems, and derive both exact
and efficient solutions. In addition to the theoretical investigation,
numerical results and real applications are used to demonstrate the superior
performance of the proposed method.
