Related papers: Unifying Practical Uncertainty Representations: I.…
Communicating forecast uncertainty effectively is a persistent challenge in predictive endeavours such as weather forecasting. This paper explores the application of possibility theory as a complementary approach to traditional probability…
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this…
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering…
We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to…
We analyze the issue of unitary equivalence within Generalized Uncertainty Principle (GUP) theories in the one-dimensional case. For a deformed Heisenberg algebra, its representation in terms of Hilbert space and conjugate operators is not…
Univariate visualizations like histograms, rug plots, or box plots provide concise visual summaries of distributions. However, each individual visualization may fail to robustly distinguish important features of a distribution, or provide…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
Conformal prediction (CP) is a popular frequentist framework for representing uncertainty by providing prediction sets that guarantee coverage of the true label with a user-adjustable probability. In most applications, CP operates on…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
As animals interact with their environments, they must infer properties of their surroundings. Some animals, including humans, can represent uncertainty about those properties. But when, if ever, do they use probability distributions to…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…
General problems in analyzing information in a probabilistic database are considered. The practical difficulties (and occasional advantages) of storing uncertain data, of using it conventional forward- or backward-chaining inference…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…