Related papers: Stochastic Unrelatedness, Couplings, and Contextua…
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…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the…
Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
Scatter plots are widely recognized as fundamental tools for illustrating the relationship between two numerical variables. Despite this, based on solid theoretical foundations, scatter plots generated from pairs of continuous random…
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space time. We explain that they are due to space time symmetries. This paper is a critical review of metaphysical conclusions found in many…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
Kolmogorov's first axiom of probability is probability takes values between 0 and 1; however, in Cox's derivation of probability having a maximum value of unity is arbitrary since he derives probability as a tool to rank degrees of…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…
Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For…
The paper deals with the order statistics and empirical mathematical expectation (which is also called the estimate of mathematical expectation in the literature) in the case of infinitely increasing random variables. The Kolmogorov concept…
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…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…