Bayesian Inference for Causal Effects: The Role of Randomization

TLDR

Causal effect estimation hinges on treatment assignment mechanisms; unless these mechanisms are ignorable, Bayesian inference must model them and can be sensitive to prior specifications, and not all ignorable mechanisms guarantee prior‑insensitive inference. The study demonstrates that classical randomized designs serve as appealing assignment mechanisms that simplify causal inference by reducing sensitivity to prior assumptions. In experiments, only one treatment assignment is observed, so Bayesian inference predicts outcomes under other assignments by modeling the predictive distribution of unobserved values.

Abstract

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 probabilistic 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. Moreover, not all ignorable mechanisms can yield data from which inferences for causal effects are insensitive to prior specifications. Classical randomized 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.