Related papers: Bayesian Probabilities and the Histories Algebra
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra.…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
It is shown how consistent histories quantum cosmology can be realised through Isham's Histories Projection Operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle…
The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of…
There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox's Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of…
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…
We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
We treat continuous histories within the histories approach to generalised quantum mechanics. The essential tool is the `history group': the analogue, within the generalised history scheme, of the canonical group of single-time quantum…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible…
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…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…