Related papers: Possibilistic inferential models: a review
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…
Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…
Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack…
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…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
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…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
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…
The framework of Inferential Models (IMs) has recently been developed in search of what is referred to as the holy grail of statistical theory, that is, prior-free probabilistic inference. Its method of Conditional IMs (CIMs) is a critical…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…
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…
Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of…
The aim of this paper is to firmly establish subjective fiducial inference as a rival to the more conventional schools of statistical inference, and to show that Fisher's intuition concerning the importance of the fiducial argument was…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…
Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM…
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty -- due to incomplete knowledge -- requires…
Reliable inference requires that artificial intelligence (AI) models provide trustworthy uncertainty estimates, not merely accurate predictions. Recent advances in Bayesian learning have made significant progress toward this goal, and…