  Estimating heterogeneous treatment effects across individuals has attracted
growing attention as a statistical tool for performing critical
decision-making. We propose a Bayesian inference framework that quantifies the
uncertainty in treatment effect estimation to support decision-making in a
relatively small sample size setting. Our proposed model places Gaussian
process priors on the nonparametric components of a semiparametric model called
a partially linear model. This model formulation has three advantages. First,
we can analytically compute the posterior distribution of a treatment effect
without relying on the computationally demanding posterior approximation.
Second, we can guarantee that the posterior distribution concentrates around
the true one as the sample size goes to infinity. Third, we can incorporate
prior knowledge about a treatment effect into the prior distribution, improving
the estimation efficiency. Our experimental results show that even in the small
sample size setting, our method can accurately estimate the heterogeneous
treatment effects and effectively quantify its estimation uncertainty.
