Adaptive Bayesian credible sets in regression with a Gaussian process prior
From MaRDI portal
Publication:895012
DOI10.1214/15-EJS1078zbMath1327.62300arXiv1504.07972OpenAlexW2962958357MaRDI QIDQ895012
Suzanne Sniekers, Aad W. van der Vaart
Publication date: 25 November 2015
Published in: Electronic Journal of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.07972
Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Nonparametric tolerance and confidence regions (62G15)
Related Items
Joint non-parametric estimation of mean and auto-covariances for Gaussian processes, Adaptive Bayesian credible bands in regression with a Gaussian process prior, Asymptotic frequentist coverage properties of Bayesian credible sets for sieve priors, Empirical Bayes oracle uncertainty quantification for regression, Adaptation bounds for confidence bands under self-similarity, Posterior contraction and credible regions for level sets, A fast and calibrated computer model emulator: an empirical Bayes approach, Rejoinder: ``Probabilistic integration: a role in statistical computation?, Comment: ``Bayes, oracle Bayes and empirical Bayes, Can We Trust Bayesian Uncertainty Quantification from Gaussian Process Priors with Squared Exponential Covariance Kernel?
Cites Work
- Unnamed Item
- On adaptive inference and confidence bands
- Bayesian inverse problems with Gaussian priors
- An analysis of Bayesian inference for nonparametric regression
- Credible sets in the fixed design model with Brownian motion prior
- Rates of contraction of posterior distributions based on Gaussian process priors
- On nonparametric confidence intervals
- On the Bernstein-von Mises theorem with infinite-dimensional parameters
- An adaptation theory for nonparametric confidence intervals
- Convergence rates of posterior distributions.
- Weak convergence and empirical processes. With applications to statistics
- Honest adaptive confidence bands and self-similar functions
- Empirical Bayes scaling of Gaussian priors in the white noise model
- Confidence bands in density estimation
- Adaptive confidence bands
- Bayesian inference with rescaled Gaussian process priors
- Adaptive confidence balls
- Adaptive nonparametric confidence sets
- Frequentist coverage of adaptive nonparametric Bayesian credible sets
- Adaptive Confidence Bands for Nonparametric Regression Functions
- A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
