Related papers: The Conditional Uncertainty Principle
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…
This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
Aleatoric uncertainty quantification seeks for distributional knowledge of random responses, which is important for reliability analysis and robustness improvement in machine learning applications. Previous research on aleatoric uncertainty…
We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing…
An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a…