Add treatment effect shocks

[tsrobinson]

One use case of synthetic data is in simulating experiments. In this context, the user may want to hypothesise that there is some treatment effect $\tau$ that acts on some outcome variable (which would be a column from the SyGNet generator).

We could create a function (called e.g. add_treatment()) which allows users to specify $\tau$, and an outcome, and then randomise observations into treatment groups. Users can then run their proposed statistical analysis on this dataset.

A more complicated version of this would be to also allow for heterogeneous treatment effects. i.e. supply a vector of treatment effects, and a corresponding matrix of subgroups.

[tsrobinson]

Add all prototypes to new submodule called sygnet_experimental.py

[tsrobinson]

For more context, assume we have the following:

• $\tilde{X}$ -- a sample from the ESS-trained SyGNet model with $n$ observations
• $\tilde{y} \in \tilde{X}$ -- some outcome of interest from the synthetic data
• $\mu, \sigma$ -- hypothesized treatment effect and noise parameters

We can simulate a scenario where:

• $d \sim \text{Binom.}(n, 1, 0.5)$
• $y' = \tilde{y} + d \times \mathcal{N}(\mu,\sigma)$

Then regress the treatment plus covariates on the modified outcome, and calculate power over repeated samples from the synthetic generator.