Related papers: Direct and approximately valid probabilistic infer…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

In applications of linear mixed-effects models, experimenters often desire uncertainty quantification for random quantities, like predicted treatment effects for unobserved individuals or groups. For example, consider an agricultural…

As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…

Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent…

Inferential models (IMs) represent a novel possibilistic approach for achieving provably valid statistical inference. This paper introduces a general framework for fusing independent IMs in a "black-box" manner, requiring no knowledge of…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…

The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…

Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

The development of large databases of material properties, together with the availability of powerful computers, has allowed machine learning (ML) modeling to become a widely used tool for predicting material performances. While confidence…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…

Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…