A key decision facing autonomous systems with access to streams of sensory data is whether to act based on current evidence or to wait for additional information that might enhance the utility of taking an action. Computing the value of information is particularly difficult with streaming high-dimensional sensory evidence. We describe a belief projection approach to reasoning about information value in these settings, using models for inferring future beliefs over states given streaming evidence. These belief projection models can be learned from data or constructed via direct assessment of parameters and they fit naturally in modular, hierarchical state inference architectures. We describe principles of using belief projection and present results drawn from an implementation of the methodology within a conversational system.