Bayesian Inference for Causal Effects: The Role of Randomization

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Causal effects are comparisons among values that would have been observed under all possible assignments of treatments to experimental units. In an experiment, one assignment of treatments is chosen and only the values under that assignment can be observed. Bayesian inference for causal effects follows from finding the predictive distribution of the values under the other assignments of treatments. This perspective makes clear the role of mechanisms that sample experimental units, assign treatments and record data. Unless these mechanisms are ignorable (known probabi-listic functions of recorded values), the Bayesian must model them in the data analysis and, consequently, confront inferences for causal effects that are sensitive to the specification of the prior distribution of the data. More-over, not all ignorable mechanisms can yield data from which inferences for causal effects are insensitive to prior specifications. Classical random-ized designs stand out as especially appealing assignment mechanisms designed to make inference for causal effects straightforward by limiting the sensitivity of a valid Bayesian analysis.