Related papers: Cournot's principle for measure-theoretic probabil…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum…
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…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically…
Probabilities is the English translation of the book Probabilit\'es Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest son Dr. Xavier Ouvrard. In this first…
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…
We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted…
By representing an event as the joint state of a detector-timer couple that interact with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events.…
The familiar "modulus squared" form of all quantum mechanical probabilities is derived from an assumption of equal a priori probabilities concerning the final states available.
We present a complex probability measure relevant for double (pairs of) states in quantum mechanics, as an extension of the standard probability measure for single states that underlies Born's statistical rule. When the double states are…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
Correlated proportions arise in longitudinal (panel) studies. A typical example is the ``opinion swing'' problem: ``Has the proportion of people favoring a politician changed after his recent speech to the nation on TV?''. Since the same…
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.