2021/10/11 by Ismaël Castillo, Castillo, Ismaël, Thibault Randrianarisoa +1 · 1 citation
Computer Science · Mathematics · #62G #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #G.3 #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2110.05265
openalex publication_date 2021/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional Pólya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions with respect to the supremum norm. For broad classes of Hölder-smooth densities, we show that the method automatically adapts to the unknown Hölder regularity parameter. We consider the question of uncertainty quantification by providing mathematical guarantees for credible sets from the obtained posterior distributions, leading to near-optimal uncertainty quantification for the density function, as well as related functionals such as the cumulative distribution function. The results are illustrated through a brief simulation study.