Related papers: The Search for Certainty: a critical assessment
A new tool is proposed for finding out the completeness limit in apparent magnitude of a magnitude-redshift sample. The technique, closely related to the statistical test proposed by Efron & Petrosian (1992), presents a real improvement…
This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in…
The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in…
A new inequality between some functional of probability distribution functions is given. The inequality is based on strict convexity of a function used in functional definition. Equality sign in the inequality gives a characteristic…
Confidence is central to safety and assurance cases: how much confidence a decision requires and how much the argument actually provides are both important questions. We present a new method for assessing probabilistic confidence in…
Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic…
We investigate how undecidability enters into computations of classical physical systems and contributes to the increase of entropy and loss of information. In actual computation with finite bit of information capacity we accept…
I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…
Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
Bruno de Finetti was one of the most convinced advocates of finitely additive probabilities. The present work describes the intellectual pro- cess that led him to support that stance and provides a detailed account both of the first paper…
In this paper, we consider the problem of making skeptical inferences for the multi-label ranking problem. We assume that our uncertainty is described by a convex set of probabilities (i.e. a credal set), defined over the set of labels.…
Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…
Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in…
In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing…
The humanities are often characterized by sociologists as having a low mutual dependence among scholars and high task uncertainty. According to Fuchs' theory of scientific change, this leads over time to intellectual and social…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
The analytical foundations of modern probability trace back to a sequence of representation theorems that reshaped functional analysis in the twentieth century. From Fr\'echet identification of linear functionals with vectors in Hilbert…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
In his Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, Rene Descartes sought ``clear and certain knowledge of all that is useful in life.'' Almost three centuries later, in ``The foundations of…