A1740
Title: Fully Bayesian synthetic control methods with sparse convex hull restriction and Gaussian process
Authors: Junwoo Jo - Kyungpook national university (Korea, South) [presenting]
Gyuhyeong Goh - Kyungpook National University (Korea, South)
Dipak Dey - UCONN (United States)
Abstract: A fully Bayesian synthetic control method is proposed that preserves the convex hull restriction of the conventional method while enabling coherent posterior inference. The approach reparameterizes the weights by introducing latent positive variables and assigning them an exact spike-and-slab prior. This construction yields a Dirichlet prior on the normalized weights, automatically respects the convex hull restriction, and allows exact zeros, thereby inducing sparsity and enhancing interpretability. A Gibbs sampling algorithm jointly updates the inclusion indicators and latent weights, resolving the dimension-changing problem via a combination of Laplace approximation and population Monte Carlo algorithm. Treatment effects are modeled with a Gaussian process prior to allow cross-time correlation. This prior flexibly captures dynamic effects and provides principled uncertainty quantification. In simulations based on a linear factor model with designed sparsity and outliers, the proposed method achieves the lowest mean squared error among competing approaches. It also delivers higher interval coverage, particularly compared with Bayesian linear models using alternative priors. Practical advantages of the approach are further illustrated in an empirical application to California's tobacco control program.
