Exchangeable Gaussian Processes for Staggered-Adoption Policy Evaluation

We study the use of exchangeable multi-task Gaussian processes (GPs) for causal inference in panel data, applying the framework to two settings: one with a single treated unit subject to a once-and-for-all treatment and another with multiple treated units and staggered treatment adoption. Our approach models the joint evolution of outcomes for treated and control units through a GP prior that ensures exchangeability across units while allowing for flexible nonlinear trends over time. The resulting posterior predictive distribution for the untreated potential outcomes of the treated unit provides a counterfactual path, from which we derive pointwise and cumulative treatment effects, along with credible intervals to quantify uncertainty. We implement several variations of the exchangeable GP model using different kernel functions. To assess prediction accuracy, we conduct a placebo-style validation within the pre-intervention window by selecting a ``fake'' intervention date. Ultimately, this study illustrates how exchangeable GPs serve as a flexible tool for policy evaluation in panel data settings and proposes a novel approach to staggered-adoption designs with a large number of treated and control units.

Gaussian Invariant Markov Chain Monte Carlo

We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that Gaussian invariant sampling can lead to ergodic estimators with improved statistical efficiency. This is due to a remarkable property of Gaussian invariance that allows us to obtain exact analytical solutions to the Poisson equation for Gaussian targets. These solutions can be used to construct efficient and easy to use control variates for variance reduction of estimators under any intractable target. We demonstrate the new samplers and estimators in several examples, including high dimensional targets in latent Gaussian models where we compare against several advanced methods and obtain state-of-the-art results. We also provide theoretical results regarding geometric ergodicity, and an optimal scaling analysis that shows the dependence of the optimal acceptance rate on the Gaussianity of the target.