Related papers: A new approach for imprecise probabilities

For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective…

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Confidence intervals for a binomial parameter or for the ratio of Poisson means are commonly desired in high energy physics (HEP) applications such as measuring a detection efficiency or branching ratio. Due to the discreteness of the data,…

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…

Persistent Stochastic Non-Interference (PSNI) was introduced to capture a quantitative security property in stochastic process algebras, ensuring that a high-level process does not influence the observable behaviour of a low-level…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

The expense of acquiring labels in large-scale statistical machine learning makes partially and weakly-labeled data attractive, though it is not always apparent how to leverage such data for model fitting or validation. We present a…

In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse…