This talk will introduce the basic principles of Bayesian reasoning, which provides a modern, rigorous, and intuitive methodology to help social scientists make better inferences from qualitative, case-study evidence.  Bayesianism provides prescriptions for rational reasoning under uncertainty, with the goal of making well-justified assessments about how strongly the information in hand supports a given explanation over rival hypotheses.  The talk will draw on coauthored work with A.E. Charman (UC Berkeley, Dept. of Physics), Social Inquiry and Bayesian Inference: Rethinking Qualitative Research (forthcoming, CUP) and will include illustrations from the author’s research on the politics of progressive taxation in Latin America.