Matched sampling, where the researcher first finds for each exposed unit(e. ga smoker)a non-exposed unit(e.g, a never-smoker)who looks exactly like theexposed unit except for the exposure, and then compares outcomes(e.g, lungcancer rates )for the matched samples of units, is an intuitive method forinferring the causal effects of exposure versus non-exposure on the collectionof units. Although intuitive, very little formal statistical work was doneexploring the utility of matched sampling for rigorous causal inference until thelate 1960s, starting with Cochran(1968). The statistical work from that timeto the early 2000s is summarized in a text, Rubin (2006), but since that timethere has been an explosion of work on such matching, primarily in socialscience. Some of these newer methods depend critically on modern computing(e.g. Diamond and Sekhon, 2013)and thus on machine learning ideas, butsome methods are a century old. This series of lectures will: review this bodyof literature; identify critical issues with some of the intuitive, butmathematically misguided, recent efforts; and focus on new methods usingrecent ideas. When evaluating procedures, we will consider the combinationof model-based adjustments on the matched samples, an idea that dates fromthe early 1970s.

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