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We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…

Probability · Mathematics 2019-07-05 Eric Joseph Hall , Markos A. Katsoulakis

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Statistics Theory · Mathematics 2022-02-14 Xiao Fang , Malay Ghosh

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…

Methodology · Statistics 2017-11-22 Andrew Gelman , Daniel Simpson , Michael Betancourt

In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is…

Methodology · Statistics 2016-10-25 Gero Walter , Frank P. A. Coolen

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Computation · Statistics 2019-11-27 Ben Mansour Dia

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

Machine Learning · Computer Science 2019-02-20 Juozas Vaicenavicius , David Widmann , Carl Andersson , Fredrik Lindsten , Jacob Roll , Thomas B. Schön

Uncertainty estimation for machine learning models is of high importance in many scenarios such as constructing the confidence intervals for model predictions and detection of out-of-distribution or adversarially generated points. In this…

Machine Learning · Computer Science 2022-05-06 Kirill Fedyanin , Evgenii Tsymbalov , Maxim Panov

Sensitivity analysis is concerned with understanding how the model output depends on uncertainties (variances) in inputs and then identifies which inputs are important in contributing to the prediction imprecision. Uncertainty determination…

Physics and Society · Physics 2017-01-04 Yueying Zhu , Qiuping Alexandre Wang , Wei Li , Xu Cai

Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…

Methodology · Statistics 2018-09-25 Fabrizio Leisen , Cristiano Villa , Stephen G. Walker

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…

Statistics Theory · Mathematics 2019-12-12 Badr-Eddine Chérief-Abdellatif , Pierre Alquier

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

Statistics Theory · Mathematics 2013-01-23 Ali Kinkhabwala

Proper confidence calibration of deep neural networks is essential for reliable predictions in safety-critical tasks. Miscalibration can lead to model over-confidence and/or under-confidence; i.e., the model's confidence in its prediction…

Machine Learning · Computer Science 2023-08-08 Shuang Ao , Stefan Rueger , Advaith Siddharthan

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

Methodology · Statistics 2026-03-23 Tiffany Cai , Philip Greengard , Ben Goodrich , Andrew Gelman

Model-form uncertainty (MFU) in assumptions made during physics-based model development is widely considered a significant source of uncertainty; however, there are limited approaches that can quantify MFU in predictions extrapolating…

Computational Engineering, Finance, and Science · Computer Science 2025-09-16 Teresa Portone , Rebekah D. White , Joseph L. Hart

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to…

Machine Learning · Computer Science 2022-12-15 Maohao Shen , Yuheng Bu , Prasanna Sattigeri , Soumya Ghosh , Subhro Das , Gregory Wornell

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Machine Learning · Statistics 2020-01-23 Nicolas Brosse , Carlos Riquelme , Alice Martin , Sylvain Gelly , Éric Moulines

Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…

Machine Learning · Computer Science 2025-01-08 Daojun Liang , Haixia Zhang , Dongfeng Yuan

Prior Networks are a recently developed class of models which yield interpretable measures of uncertainty and have been shown to outperform state-of-the-art ensemble approaches on a range of tasks. They can also be used to distill an…

Machine Learning · Computer Science 2020-12-10 Andrey Malinin , Sergey Chervontsev , Ivan Provilkov , Mark Gales

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…

Methodology · Statistics 2015-02-24 P. Richard Hahn

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…

Machine Learning · Computer Science 2019-08-15 Qingyang Wu , He Li , Lexin Li , Zhou Yu