  Recently, conditional average treatment effect (CATE) estimation has been
attracting much attention due to its importance in various fields such as
statistics, social and biomedical sciences. This study proposes a partially
linear nonparametric Bayes model for the heterogeneous treatment effect
estimation. A partially linear model is a semiparametric model that consists of
linear and nonparametric components in an additive form. A nonparametric Bayes
model that uses a Gaussian process to model the nonparametric component has
already been studied. However, this model cannot handle the heterogeneity of
the treatment effect. In our proposed model, not only the nonparametric
component of the model but also the heterogeneous treatment effect of the
treatment variable is modeled by a Gaussian process prior. We derive the
analytic form of the posterior distribution of the CATE and prove that the
posterior has the consistency property. That is, it concentrates around the
true distribution. We show the effectiveness of the proposed method through
numerical experiments based on synthetic data.
