相关论文: A Collection of Probabilistic Hidden-Variable Theo…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
We explain the concept of p-values presupposing only rudimentary probability theory. We also use the occasion to introduce the notion of p-function, so that p-values are values of a p-function. The explanation is restricted to the discrete…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
The common cause principle for two random variables $A$ and $B$ is examined in the case of causal insufficiency, when their common cause $C$ is known to exist, but only the joint probability of $A$ and $B$ is observed. As a result, $C$…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
This paper furthers the long historical examination of and debate on the foundations of quantum mechanics (QM) by presenting two local hidden variable (LHV) rules in the context of the EPRB experiment which violate Bell's inequality, but…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim…
Usually the 'hidden variables' of Bell's theorem are supposed to describe the pair of Bell particles. Here a semantic shift is proposed, namely to attach the hidden variables to a stochastic medium or field in which the particles move. It…
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them…
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.