Related papers: Weakly Consistent Extensions of Lower Previsions
In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of $n$-coherent and $n$-convex conditional previsions, at the varying of $n$. We investigate which such previsions are the…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
Observable games are game situations that reach one of possibly many Nash equilibria. Before an instance of the game starts, an external observer does not know, a priori, what is the exact profile of actions that will occur; thus, he…
We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt…
We define and study the independent natural extension of two local uncertainty models for the general case of infinite spaces, using the frameworks of sets of desirable gambles and conditional lower previsions. In contrast to Miranda and…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
In this paper we discuss the consistency concept of Williams coherence for imprecise conditional previsions, presenting a variant of this notion, which we call W-coherence. It is shown that W-coherence ensures important consistency…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…
We study probabilistically informative (weak) versions of transitivity, by using suitable definitions of defaults and negated defaults, in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults…
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…
In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. We show that convex previsions are related with a concept of…
We give an extension of de Finetti's concept of coherence to unbounded (but real-valued) random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to…
We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…