11:30 am–12:30 pm
Jones 303 5747 S. Ellis Ave
Peter McCullagh
Department of Statistics
University of Chicago
Title: Causal Inference Versus Stochastic Models
Abstract: The classical statistical model is a stochastic process, which means a probability distribution on the space of outcomes. Sampling distributions and distributional properties of derived summaries follow from the process. Logical positivism in the sense of von Mises reverses the natural order, beginning with an outcome variable or kollektiv, from which probabilities are defined as limiting frequencies. Causal inference is based on the same frequency definition supplemented by random sampling. These notions of probability are in conflict, even when limiting frequencies exist. Accordingly, all derived concepts such as expectation, independence, random variable, and treatment effect are also in conflict. Broadly speaking, the frequentist concept is adequate for sample surveys and other areas of application such as auditing, where the population is concrete, finite, and accessible for simple random sampling. These conditions are not met in typical scientific research work, where the population is abstract, infinite and only partially accessible. The emphasis in this talk is on stochastic regression models, where random sampling does not arise, treatment assignment is associated with a Markov kernel, and the treatment effect is a group action on the parameter space.