Related papers: General Belief Measures
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Recent discussions on alternative facts, fake news, and post truth politics have motivated research on creating technologies that allow people not only to access information, but also to assess the credibility of the information presented…
As a modern approach for the foundation of quantum theory, existing studies of General Probabilistic Theories gave various models of states and measurements that are quite different from quantum theory. In this paper, to seek a more…
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. But in the last decades, several attempts to interpret it from a…
According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
Many organizations describe their processes as consensus-driven, but there is no consensus on the definition of consensus. Qualitative definitions of consensus prioritize social phenomena like "unity" that are not necessarily measurable.…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
In research policy, effective measures that lead to improvements in the generation of knowledge must be based on reliable methods of research assessment, but for many countries and institutions this is not the case. Publication and citation…
This paper contributes a novel embedding model which measures the probability of each belief $\langle h,r,t,m\rangle$ in a large-scale knowledge repository via simultaneously learning distributed representations for entities ($h$ and $t$),…
Models of opinion dynamics play a major role in various disciplines, including economics, political science, psychology, and social science, as they provide a framework for analysis and intervention. In spite of the numerous mathematical…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to…
A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are…