Related papers: A geometric approach to conditioning belief functi…

Imaging is a form of probabilistic belief change which could be employed for both revision and update. In this paper, we propose a new framework for probabilistic belief change based on imaging, called Expected Distance Imaging (EDI). EDI…

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…

The investigation of uncertainty is of major importance in risk-critical applications, such as medical image segmentation. Belief function theory, a formal framework for uncertainty analysis and multiple evidence fusion, has made…

We show how the AGM framework for belief change (expansion, revision, contraction) can be extended to deal with conditioning in the so-called Desirability-Indifference framework, based on abstract notions of accepting and rejecting options,…

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…

The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…

Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with…

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our framework and the framework of empirical coordination developed in [1].…

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…

This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use…

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates…

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…

In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients.…

Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…

Large language models (LLMs) often exhibit a puzzling disconnect between their asserted confidence and actual problem-solving competence. We offer a mechanistic account of this decoupling by analyzing the geometry of internal states across…