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Probabilistic programming systems (PP systems) allow developers to model stochastic phenomena and perform efficient inference on the models. The number and adoption of probabilistic programming systems is growing significantly. However, there is no prior study of bugs in these systems and no methodology for systematically testing PP systems. Yet, testing PP systems is highly non-trivial, especially when they perform approximate inference. In this paper, we characterize 118 previously reported bugs in three open-source PP systems—Edward, Pyro and Stan—and pro- pose ProbFuzz, an extensible system for testing PP systems. Prob- Fuzz allows a developer to specify templates of probabilistic models, from which it generates concrete probabilistic programs and data for testing. ProbFuzz uses language-specific translators to generate these concrete programs, which use the APIs of each PP system …