The paper presents our attempt to define the concept of factorization within the Dempster-Shafer theory of evidence. In the same way as in probability theory, the introduced concept can support procedures for efficient multidimensional model construction and processing. The main result of this paper is a factorization lemma describing, in the same way as in probability theory, the relationship ...

In many classic problems of asymptotic analysis, it appears that the scaled average of a sequence of F -distributed random variables converges to G-distributed limit in some sense of convergence. In this paper, we look at the classic convergence problems from a novel perspective: we aim to characterize all possible limits of the sum of a sequence of random variables under different choices of d...

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­‐ additive has conditional probabilities that fail to be conglomerable i...

The paper introduces (in our knowledge first) attempt to define the concept of factorization within the Dempster-Shafer theory of evidence. In the same way as in probability theory, the presented concept can support procedures for efficient multidimensional model construction and processing. The main result of this paper is a factorization lemma describing, in the same way as in probability the...

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While is an important resource, only a subset of entangled have entropy. In this work, we characterize the class density matrices h...

Abstract—The problems of conditional entropy’s definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented. Examples are given to prove the conclusion that conditional entropy never be increased is not absolute, thus the representation that information is to decrease uncertainty in the definition of informati...

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any co...

It is often stated in papers tackling the task of selecting a Bayesian network structure from data that there are these two distinct approaches: (i) Apply conditional indepen­ dence tests . when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete data and a given node ordering this division is largely a myth, by show...

This paper presents axioms for systems of conditional preferences and provides representation results for these systems. It reports on a new way of representing a system of conditional preferences, by means of a system of conditional lexicographic probabilities (SCLP) (cf. Asheim and Perea, Games and Economic Behavior, forthcoming). An SCLP ensures well-defined conditional beliefs representing ...