相关论文: Gibbs conditioning extended, Boltzmann conditionin…
Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…
We liberate Equilibrium Propagation (EP) from the limit of infinitesimal perturbations by establishing a finite-nudge foundation for local credit assignment. By modeling network states as Gibbs-Boltzmann distributions rather than…
This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES)…
In this paper we give a conditional improvement to the Elekes-Szab\'{o} problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}[x,y,z]$ belonging to a particular family of…
Both, Bayes Theorem and the cMPE-Method serve for establishing relations between systems of probabilities. By the cMPE-Method non-conditional probabilities are added, by the DPE-Method, they are subtracted, however, in both versions…
After a brief introduction to Probability Bracket Notation (PBN), indicator operator and conditional density operator (CDO), we investigate probability spaces associated with various quantum systems: system with one observable (discrete or…
This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…
In [A dozen de {F}inetti-style results in search of a theory, Ann. Inst. H. Poincar\'{e} Probab. Statist. 23(2)(1987), 397--423], Diaconis and Freedman studied low-dimensional projections of random vectors from the Euclidean unit sphere and…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Expectation Propagation (Minka, 2001) is a widely successful algorithm for variational inference. EP is an iterative algorithm used to approximate complicated distributions, typically to find a Gaussian approximation of posterior…
We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random…
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new…
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…
It is well know that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem, but checking the validity of these becomes trickier when we switch to compound and iterated…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
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…
Existence and uniqueness results for the solution of the Gibbs-type formula from non-extensive mechanics are derived rigorously. A new conditional extremal problem is proposed to get in a more simple way the Gibbs-type formula itself.
A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the…
In this paper, we present event constraints as a new modeling paradigm that generalizes joint chance constraints from stochastic optimization to (1) enforce a constraint on the probability of satisfying a set of constraints aggregated via…