Related papers: Parameter estimation with a class of outer probabi…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due…

Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…

It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

The Dempster-Shafer theory of evidence has been used intensively to deal with uncertainty in knowledge-based systems. However the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is…

Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using…

Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…

We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…

Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…