Related papers: Calibrating general posterior credible regions

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model…

Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty.…

In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general…

We present a novel Bayesian model and a corresponding robust, probabilistic calibration procedure for the CORSAIR polarimeter that can be applied to other polarimeters. Our calibration procedure combines existing Mueller matrix…

We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…

Confidence region prediction is a practically useful extension to the commonly studied pattern recognition problem. Instead of predicting a single label, the constraint is relaxed to allow prediction of a subset of labels given a desired…

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

Existing inferential methods for small area data involve a trade-off between maintaining area-level frequentist coverage rates and improving inferential precision via the incorporation of indirect information. In this article, we propose a…

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…

This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes…

Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…

Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile…

Conformal prediction is a popular framework of uncertainty quantification that constructs prediction sets with coverage guarantees. To uphold the exchangeability assumption, many conformal prediction methods necessitate an additional…

Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…

Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex non-linear models with intractable likelihoods. However, posterior approximations obtained with SBI are often…