An optimal transport-based generative model for Bayesian posterior sampling
Ke Li, Wei Han, Yuexi Wang, Yun Yang · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2026
Abstract We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Building on transport map-based generative models for posterior sampling, we propose an optimal transport (OT)-constrained transport map class that learns a deterministic map from a reference distribution to the target posterior through constrained optimization. The proposed class exploits structural properties of OT maps and allows efficient generation of many independent, high-quality posterior samples. The framework supports both continuous and mixed discrete–continuous parameter spaces, with specific adaptations for latent variable models and near-Gaussian posteriors. Beyond computational benefits, it also enables new inferential tools based on OT-derived multivariate ranks and quantiles for Bayesian exploratory analysis and visualization. We demonstrate the effectiveness of our approach through multiple simulation studies and a real-world data analysis.