Related papers: Calibrating dependence between random elements
Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are some options to handle the estimation of each component's reliability.…
A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…
The rate at which dependencies between future and past observations decay in a random process may be quantified in terms of mixing coefficients. The latter in turn appear in strong laws of large numbers and concentration of measure results…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
In 1960 R\'enyi in his Michigan State University lectures asked for the number of random queries necessary to recover a hidden bijective labeling of $n$ distinct objects. In each query one selects a random subset of labels and asks, which…
An important task in the field of sensor technology is the efficient implementation of adaptation procedures of measurements from one sensor to another sensor of identical design. One idea is to use the estimation of an affine…
In environmental sciences, it is often of interest to assess whether the dependence between extreme measurements has changed during the observation period. The aim of this work is to propose a statistical test that is particularly sensitive…
In two previous experiments we investigated the neural precursors of subjects' "free" choices for one of two options (pressing one of two buttons, and choosing between adding and subtracting numbers). In these experiments the distribution…
This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the…
Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…
This paper suggests five measures of association between two random vectors X = (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore invariant with respect to the marginal distributions of the components X_i and Y_j.…
Successful realization of Bell tests has settled an 80-year-long debate, proving the existence of correlations which cannot be explained by a local realistic model. Recent experimental progress allowed to rule out any possible loopholes in…
We revisit the classical broken sample problem: Two samples of i.i.d. data points $\mathbf{X}=\{X_1,\cdots, X_n\}$ and $\mathbf{Y}=\{Y_1,\cdots,Y_m\}$ are observed without correspondence with $m\leq n$. Under the null hypothesis,…
This note proves a weak type of the sharpness principle as conjectured by Gneiting, Balabdaoui, and Raftery in 2007 in connection with probabilistic forecasting subject to calibration constraints. A strong version of such a principle still…
Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately…
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is…
Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot…
The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in quantum cryptography, complexity theory,…