Pólya tree posterior distributions on densities

DOI10.1214/16-AIHP784zbMath1384.62156MaRDI QIDQ1700406

Ismaël Castillo

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aihp/1511773739

zbMATH Keywords

Bernstein-von Mises theoremBayesian nonparametricsminimax rateBayesian Donsker theoremPólya tree distributionsupremum norm convergence

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Bayesian inference (62F15) Nonparametric tolerance and confidence regions (62G15)

Related Items (16)

Adaptive Bayesian density estimation in sup-norm ⋮ A nonparametric Bayesian approach to copula estimation ⋮ Smoothing and adaptation of shifted Pólya tree ensembles ⋮ Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions ⋮ Hidden Markov Pólya Trees for High-Dimensional Distributions ⋮ Bernstein-type bounds for beta distribution ⋮ Random tree Besov priors -- towards fractal imaging ⋮ Posterior concentration for Bayesian regression trees and forests ⋮ Efficient nonparametric Bayesian inference for \(X\)-ray transforms ⋮ On the Bernstein-von Mises theorem for the Dirichlet process ⋮ A review of uncertainty quantification for density estimation ⋮ Uncertainty quantification for Bayesian CART ⋮ Spike and slab Pólya tree posterior densities: adaptive inference ⋮ Bernstein-von Mises theorems for statistical inverse problems. II: Compound Poisson processes ⋮ Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation ⋮ Optional Pólya trees: posterior rates and uncertainty quantification

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