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Fairfield and Charman provide a modern, rigorous and intuitive methodology for case-study research to help social scientists and analysts make better inferences from qualitative evidence. The book develops concrete guidelines for conducting inference to best explanation given incomplete information; no previous exposure to Bayesian analysis or specialized mathematical skills are needed. Topics covered include constructing rival hypotheses that are neither too simple nor overly complex, assessing the inferential weight of evidence, counteracting cognitive biases, selecting cases, and iterating between theory development, data collection, and analysis. Extensive worked examples apply Bayesian guidelines, showcasing both exemplars of intuitive Bayesian reasoning and departures from Bayesian principles in published case studies drawn from process-tracing, comparative, and multimethod research. Beyond improving inference and analytic transparency, an overarching goal of this book is to revalue qualitative research and place it on more equal footing with respect to quantitative and experimental traditions by illustrating that Bayesianism provides a universally applicable inferential framework.