Related papers: Principle conditioning
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
A very simple example demonstrates that Fisher's application of the conditionality principle to regression ("fixed-$x$ regression"), endorsed by Sprott and many other followers, makes prediction impossible in the context of statistical…
There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$,…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…
In a series of essays, beginning with this article, we are going to develop a new formulation of micro-phenomena based on the principles of reality and causality. The new theory provides with us a new depiction of micro-phenomena assuming…
This is a non-technical introduction into theory of contextuality. More precisely, it presents the basics of a theory of contextuality called Contextuality-by-Default (CbD). One of the main tenets of CbD is that the identity of a random…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
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…
The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of a…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…