Optional Pólya trees: posterior rates and uncertainty quantification
From MaRDI portal
Publication:2106798
DOI10.1214/22-EJS2086MaRDI QIDQ2106798
Thibault Randrianarisoa, Ismaël Castillo
Publication date: 19 December 2022
Published in: Electronic Journal of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.05265
Bayesian nonparametricsuncertainty quantificationsupremum normPólya treesfrequentist coverage of credible setsposterior convergence rates
Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)
Cites Work
- Unnamed Item
- Unnamed Item
- BART: Bayesian additive regression trees
- Supremum norm posterior contraction and credible sets for nonparametric multivariate regression
- Nonparametric Bernstein-von Mises theorems in Gaussian white noise
- Rates of contraction for posterior distributions in \(L^{r}\)-metrics, \(1 \leq r \leq \infty\)
- On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
- On Bayesian supremum norm contraction rates
- On adaptive inference and confidence bands
- Adaptive Bernstein-von Mises theorems in Gaussian white noise
- Uniform limit theorems for wavelet density estimators
- On adaptive posterior concentration rates
- Optional Pólya tree and Bayesian inference
- Inequalities for the gamma function
- On nonparametric confidence intervals
- Adaptive shrinkage in Pólya tree type models
- Pólya tree posterior distributions on densities
- Honest confidence regions for nonparametric regression
- Convergence rates of posterior distributions.
- Honest adaptive confidence bands and self-similar functions
- Uncertainty quantification for Bayesian CART
- Spike and slab Pólya tree posterior densities: adaptive inference
- Adaptive Bayesian density estimation in sup-norm
- Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
- Posterior concentration for Bayesian regression trees and forests
- Minimax optimal rates for Mondrian trees and forests
- A random forest guided tour
- Comments on: ``A random forest guided tour
- Smoothing and adaptation of shifted Pólya tree ensembles
- Coupling Optional Pólya Trees and the Two Sample Problem
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- A Bayesian CART algorithm
- Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity
- Real Analysis and Probability
- A Bayesian Hierarchical Model for Related Densities by using Pólya Trees
- Fundamentals of Nonparametric Bayesian Inference
