  We develop a Gaussian-process mixture model for heterogeneous treatment
effect estimation that leverages the use of transformed outcomes. The approach
we will present attempts to improve point estimation and uncertainty
quantification relative to past work that has used transformed variable related
methods as well as traditional outcome modeling. Earlier work on modeling
treatment effect heterogeneity using transformed outcomes has relied on tree
based methods such as single regression trees and random forests. Under the
umbrella of non-parametric models, outcome modeling has been performed using
Bayesian additive regression trees and various flavors of weighted single
trees. These approaches work well when large samples are available, but suffer
in smaller samples where results are more sensitive to model misspecification -
our method attempts to garner improvements in inference quality via a correctly
specified model rooted in Bayesian non-parametrics. Furthermore, while we begin
with a model that assumes that the treatment assignment mechanism is known, an
extension where it is learnt from the data is presented for applications to
observational studies. Our approach is applied to simulated and real data to
demonstrate our theorized improvements in inference with respect to two causal
estimands: the conditional average treatment effect and the average treatment
effect. By leveraging our correctly specified model, we are able to more
accurately estimate the treatment effects while reducing their variance.
