Projection inferences are inferences about speaker commitment to a content embedded under an entailment-canceling operator, for example in polar interrogatives with clause-embedding predicates (Does John know that Julian dances salsa?). Speaker commitment to embedded content is modulated by multiple factors, including the predicate, interlocutors' prior beliefs about the content, and its at-issueness. We propose an RSA model of projection inferences in such environments. Crucially, we take the interpretive procedure to involve inferring a speaker's and attitude holder's belief in the content. In a behavioral study, we investigate inferred beliefs about contents embedded under the predicates “think” and “know” that listeners ascribe to the speaker and a potential attitude holder. We use the empirical data to parametrize the model. The resulting predictions mirror some, but not all, of the qualitative empirical patterns. This is a first step towards a systematic analysis of projection inferences using probabilistic pragmatic models.