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Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centred Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence…
A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…
Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…
In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac's sphere, which are obtained as the law of a vector of $N$ i.i.d. variables after it is rescaled to have unit average…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
The inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space $z > 0$ has been discovered by McKean and then independently re-discovered by Cornell et. al. The essence of this phenomenon is that…
We revisit classic balancing problems for linear extensions of a partially ordered set $P$, proving results that go far beyond many of the best earlier results on this topic. For example, with $p(x\prec y)$ the probability that $x$ precedes…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
In two recent papers we introduced some new techniques for constructing an extension of a probability-preserving system $T:\mathbb{Z}^d\curvearrowright (X,\mu)$ that enjoys certain desirable properties in connexion with the asymptotic…
In this study, we precisely evaluated the feasibility of the chaotic inflation model within a non-canonical kinetic framework. By applying the slow-roll approximation and imposing constraints on the equilateral non-Gaussianity $f_{\rm…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…