Related papers: Quantization for a probability distribution genera…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
We present a new method to measure the work $w$ performed on a driven quantum system and to sample its probability distribution $P(w)$. The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The…
Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
Previously, the author offered a plasma-like description of quantum phenomena. This article offers a new criterion of approximation of probability density functions of quantum theories by sums of $\delta$-functions with integer coefficients…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…
Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create…
Given a computable probability measure P over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of P.