Related papers: Safe Probability
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
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…
The plausibility of uncommon events and miracles based on testimony of such an event has been much discussed. When analyzing the probabilities involved, it has mostly been assumed that the common events can be taken as data in the…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
The Monty Hall problem is a classic probability puzzle known for its counterintuitive solution, revealing fundamental discrepancies between mathematical reasoning and human intuition. To bridge this gap, we introduce a novel explanatory…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
We propose a new approach to promote safety in classification tasks with established concepts. Our approach -- called a conceptual safeguard -- acts as a verification layer for models that predict a target outcome by first predicting the…
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…
An assurance case is intended to provide justifiable confidence in the truth of its top claim, which typically concerns safety or security. A natural question is then "how much" confidence does the case provide? We argue that confidence…