Gregor Steiner and Mark Steel’s contribution to the Discussion of ‘Parameterizing and Simulating from Causal Models’ by Evans and Didelez’

We congratulate the authors on a very interesting and thought-provoking paper, which will certainly have an impact on causal modelling.While the authors focus on inference with likelihood-based methods, they only briefly mention Bayesian methods.We wish to touch upon Bayesian inference in this comment.Frugal parameterizations are typically variation-free and in a Bayesian context the concept of "variation-freeness" naturally extends to prior independence (see Florens et al. [1990]).This is crucial for the concept of a "Bayesian cut" and is often very helpful to formulate a sensible prior.Consider the simple model with outcome Y , binary treatment X, and confounder Z with distributionsZ ), X | Z = z ∼ Ber(expit(z)), Y | do(X = x) ∼ N (α + βx, σ 2 ).