Parameterizing and Simulating from Causal Models

Abstract Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, object of interest is often marginal quantity this distribution. This creates many practical complications for inference, even where problem non-parametrically identified. In particular, it difficult to perform likelihood-based or simulate model general way. We introduce ‘frugal parameterization’, places effect at its centre, and then builds rest around it. do way that provides recipe constructing regular, non-redundant parameterization using quantities interest. case discrete variables we can use odds ratios complete parameterization, while continuous copulas natural choice; possibilities also discussed. Our methods allow us construct models with parametrically specified distributions, fit them methods, including fully Bayesian approaches. proposal includes parameterizations average treatment on treated, well