Calibrating general posterior credible regions

Abstract

An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no guarantee that such regions will achieve the nominal frequentist coverage probability, even approximately. To overcome this difficulty, we propose a general strategy that introduces an additional scalar tuning parameter to control the posterior spread, and we develop an algorithm that chooses this parameter so that the corresponding credible region achieves the nominal coverage probability.

15 pages, including supplementary material; 2 figures, 3 tables

References in corpus (8)

• Variational Inference: A Review for Statisticians
• An MCMC Approach to Classical Estimation
• From $\epsilon$-entropy to KL-entropy: Analysis of minimum information complexity density estimation
• Bayesian empirical likelihood for quantile regression
• Gibbs posterior for variable selection in high-dimensional classification and data mining
• On the properties of variational approximations of Gibbs posteriors
• Gibbs posterior inference on the minimum clinically important difference
• A Sandwich Likelihood Correction for Bayesian Quantile Regression based on the Misspecified Asymmetric Laplace Density

Cited by in corpus (30)

• User-friendly introduction to PAC-Bayes bounds
• False confidence, non-additive beliefs, and valid statistical inference
• A comparison of learning rate selection methods in generalized Bayesian inference
• Gibbs posterior concentration rates under sub-exponential type losses
• Can I Trust My Fairness Metric? Assessing Fairness with Unlabeled Data and Bayesian Inference
• Model-free posterior inference on the area under the receiver operating characteristic curve
• Safe-Bayesian Generalized Linear Regression
• Gibbs posterior inference on multivariate quantiles
• Function-on-Scalar Quantile Regression with Application to Mass Spectrometry Proteomics Data
• Empirical priors and coverage of posterior credible sets in a sparse normal mean model
• Robust Inference and Model Criticism Using Bagged Posteriors
• Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image
• Generalised likelihood profiles for models with intractable likelihoods
• A reduced-rank approach to predicting multiple binary responses through machine learning
• Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior
• Generalized Bayesian Likelihood-Free Inference
• High-dimensional sparse classification using exponential weighting with empirical hinge loss
• Empirical priors for prediction in sparse high-dimensional linear regression
• Concentration properties of fractional posterior in 1-bit matrix completion
• Gaussian Mixture Models for Blended Photometric Redshifts
• Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix
• Empirical Bayes inference in sparse high-dimensional generalized linear models
• Calibrating generalized predictive distributions
• Computationally efficient variational-like approximations of possibilistic inferential models
• Semiparametric inference using fractional posteriors
• Generalized Bayes Approach to Inverse Problems with Model Misspecification
• Statistical Inference for Bayesian Risk Minimization via Exponentially Tilted Empirical Likelihood
• Robust posterior inference for Youden's index cutoff
• Generalized Posterior Calibration via Sequential Monte Carlo Sampler
• Weighted Particle-Based Optimization for Efficient Generalized Posterior Calibration