Related papers: Generalized probabilities in statistical theories
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
We survey the development of probability from 1900, starting with Bachelier's theory of speculation. Fisher information appears in the theory of estimation. We touch on Brownian motion, and the Wiener integral. The Ito calculus, and its…
The framework of generalized probabilistic theories (GPT) is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a…
We discuss some issues about probability in quantum mechanics, with particular emphasis on the GHZ theorem. We propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for systems where…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory,…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
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…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schr\"odinger equation.…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is…