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This paper focuses on two mathematical topics, namely continuous probability distributions (CPD) and integral calculus (IC). These two sectors that are linked by a formula are quite compartmented in teaching classes in France. The main…
Individual events at high-energy colliders like the LHC can be represented by a sequence of measurements, or 'point patterns' in an observable space. Starting from this data representation, we build a simple Bayesian probabilistic model for…
We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
Talagrand's inequalities make a link between two fundamentals concepts of probability: transport of measures and entropy. The study of the counterpart of these inequalities in the context of free probability has been initiated by Biane and…
We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…
This work considers Bayesian inference under misspecification for complex statistical models comprised of simpler submodels, referred to as modules, that are coupled together. Such ``multi-modular" models often arise when combining…
In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…
Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…
Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined…
A vast array of transformative technologies developed over the past decade has enabled measurement and perturbation at ever increasing scale, yet our understanding of many systems remains limited by experimental capacity. Overcoming this…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound…
Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a change in perspective that shifts the…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
This chapter reviews the microeconometrics literature on partial identification, focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions…
The principle of optimism in the face of uncertainty underpins many theoretically successful reinforcement learning algorithms. In this paper we provide a general framework for designing, analyzing and implementing such algorithms in the…
This article develops a Bayesian approach for estimating panel quantile regression with binary outcomes in the presence of correlated random effects. We construct a working likelihood using an asymmetric Laplace (AL) error distribution and…
The catch-up effect and the Matthew effect offer opposing characterizations of globalization: the former predicts an eventual convergence as the poor can grow faster than the rich due to free exchanges of complementary resources, while the…
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the…