Synthetic data to approximate real datasets

[finnhacks42]

Since we can't evaluate the performance of observational causal inference directly via cross-val, one approach to deciding which algorithm and approach to use is to test how the options perform on synthetic data that has similar properties to the real data. This means replicating;

• correlational relationships between confounders
• marginal distributions over all variables
• strength of relationships between confounders and treatment (eg propensity score aroc)
• generating a known response surface y = f(X,T) + epsilon with a specified maximal achievable r2.

[dsteinberg]

See the simulations folder for some simple DGPs

[dsteinberg]

I'll make better simulations as a "nice to have" for now