相关论文: When Index Term Probability Violates the Classical…

Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…

According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…

Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…

We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction…

This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…

According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the…

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…

We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…

A large number of studies in cognitive science have revealed that probabilistic outcomes of certain human decisions do not agree with the axioms of classical probability theory. The field of Quantum Cognition provides an alternative…

Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…

Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical…

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…

This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…

Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…

Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…

This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…