Discourse relations can either be explicitly marked by discourse connectives (DCs), such as therefore and but, or implicitly conveyed in natural language utterances. How speakers choose between the two options is a question that is not well understood. In this study, we propose a psycholinguistic model that predicts whether or not speakers will produce an explicit marker given the discourse relation they wish to express. Our model is based on two information-theoretic frameworks: (1) the Rational Speech Acts model, which models the pragmatic interaction between language production and interpretation by Bayesian inference, and (2) the Uniform Information Density theory, which advocates that speakers adjust linguistic redundancy to maintain a uniform rate of information transmission. Specifically, our model quantifies the utility of using or omitting a DC based on the expected surprisal of comprehension, cost of production, and availability of other signals in the rest of the utterance. Experiments based on the Penn Discourse Treebank show that our approach outperforms the state-of-the-art performance at predicting the presence of DCs (Patterson and Kehler, 2013), in addition to giving an explanatory account of the speaker’s choice.