Related papers: A new approach for imprecise probabilities
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
The main contribution of this paper is a mathematical definition of statistical sparsity, which is expressed as a limiting property of a sequence of probability distributions. The limit is characterized by an exceedance measure~$H$ and a…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
In genomics, differential abundance and expression analyses are complicated by the compositional nature of sequence count data, which reflect only relative-not absolute-abundances or expression levels. Many existing methods attempt to…
We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level,…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is…
We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Prediction-powered inference (PPI) is a recent framework for valid statistical inference with partially labeled data, combining model-based predictions on a large unlabeled set with bias correction from a smaller labeled subset. Building on…