Credible intervals with Bayesian Causal Forest in Python

[d-vct]

Hello ! I am using the Bayesian Causal Forest method to perform causal inference. I was wondering if it is possible to retrieve credible intervals for the CATE and the potential outcomes. It seems that we can only retrieve the point estimates. Thank you!

[andrewherren]

Hi there, thanks for reaching out!

The sample() method of the BCFModel object returns posterior draws of the CATE function ($\tau(X)$ in the BCF paper notation), accessible as tau_hat_train (and tau_hat_test if you provided a test set when calling sample). These posterior draws can be used to compute point estimates such as a posterior mean, but also a credible interval.

As a quick demo, suppose you've fit a BCFModel as in the python causal vignette

bcf_model = BCFModel()
bcf_model.sample(X_train, Z_train, y_train, pi_train, X_test, Z_test, pi_test)

You can compute the posterior mean for the train and test sets as follows

tau_hat_train_mean = np.mean(bcf_model.tau_hat_train, axis = 1)
tau_hat_test_mean = np.mean(bcf_model.tau_hat_test, axis = 1)

Similarly, you can compute the 2.5th and 97.5th percentiles that define a 95% credible interval as follows

tau_hat_train_ci_lb = np.percentile(bcf_model.tau_hat_train, 2.5, axis=1)
tau_hat_test_ci_lb = np.percentile(bcf_model.tau_hat_test, 2.5, axis=1)
tau_hat_train_ci_ub = np.percentile(bcf_model.tau_hat_train, 97.5, axis=1)
tau_hat_test_ci_ub = np.percentile(bcf_model.tau_hat_test, 97.5, axis=1)

[d-vct]

Thank you for your quick response! And thank you for the Python implementation, it's very useful.