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The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
The setting of a right-censored random sample subject to contamination is considered. In various fields, expert information is often available and used to overcome the contamination. This paper integrates expert knowledge into the…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
Recently we have introduced a novel characterisation of the distribution of twin primes that consists of three essential elements. These are: that the twins are most naturally viewed as a subsequence of the primes themselves, that the…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…
The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…
The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…
Population attributable fractions aim to quantify the proportion of the cases of an outcome (for example, a disease) that would have been avoided had no individuals in the population been exposed to a given exposure. This quantity thus…
Random-effects models are central to meta-analysis, yet the between-study variance is often underestimated when the number of studies is small. In such settings, confidence intervals become unduly narrow and fail to attain the nominal…
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
The task of analyzing extreme events with censoring effects is considered under a framework allowing for random covariate information. A wide class of estimators that can be cast as product-limit integrals is considered, for when the…
In research policy, effective measures that lead to improvements in the generation of knowledge must be based on reliable methods of research assessment, but for many countries and institutions this is not the case. Publication and citation…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
In this study, we introduce a new approach to statistical decision theory. Without using a loss function, we select good decision rules to choice between two hypotheses. We call them "experts". They are globally unbiased but also…