Related papers: A Bayesian Analogue of Gleason's Theorem
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schr"dinger's Cat…
In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of "quantum theory from five reasonable axioms." Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
How should we model an observer within quantum mechanics or quantum field theory? How can classical physics emerge from a quantum model, and why should classical probability be useful? How can we model a selective measurement entirely…
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s…
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…
Probabilities enter quantum mechanics via Born's rule, the uniqueness of which was proven by Gleason. Busch subsequently relaxed the assumptions of this proof, expanding its domain of applicability in the process. Extending this work to…
This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…
This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…
Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches,…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from…
Recently quantum prediction problem was proposed in the Bayesian framework. It is shown that Bayesian predictive density operators are the best predictive density operators when we evaluate them by using the average relative entropy based…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
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…
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…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…