Related papers: Consistent transformations of belief functions
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…
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…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
Large language models (LLMs) are increasingly used to simulate human behavior, but common practices to use LLM-generated data are inefficient. Treating an LLM's output ("model choice") as a single data point underutilizes the information…
Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers…
For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…
There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Schervish et al. 2009, Pettigrew 2016). However, this…
Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…
Large Language Models (LLMs) are expected to be predictable and trustworthy to support reliable decision-making systems. Yet current LLMs often show inconsistencies in their judgments. In this work, we examine logical preference consistency…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
Constructing valid confidence sets is a crucial task in statistical inference, yet traditional methods often face challenges when dealing with complex models or limited observed sample sizes. These challenges are frequently encountered in…