Related papers: A Short Survey on Bounding the Union Probability u…
Unit-level models for survey data offer many advantages over their area-level counterparts, such as potential for more precise estimates and a natural benchmarking property. However two main challenges occur in this context: accounting for…
A problem dating back to Boole [Laws of Thought, Walton & Maberly,1854] is what can be computed about the probability of a finite union of events when given as input the probabilities of intersections of some of the events. The modern…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
We discuss how to determine and combine upper limits based on observed events and estimated backgrounds with a Bayesian method, when insignificant signals are observed in independent measurements. In addition to some general features…
In this paper, we first describe the generalized notion of Cramer-Rao lower bound obtained by Naudts (2004) using two families of probability density functions, the original model and an escort model. We reinterpret the results in Naudts…
In this paper alternative formulations of the conventional uncertainty relation are studied in the context of decoherent histories. The results are given in terms of Shannon information. A variety of methods are developed to evaluate the…
In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in uncertain theories (such as: fuzzy, neutrosophic and extensions) to the Over/Under/Off Mass that could be used in Information Fusion. The approach…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.
In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated…
Extensions of the Boole--Frechet inequalities give sharp bounds for the probabilities of compound events, particularly when only the probabilities of atomic events (that make up the compound events) are known. We present a constructive…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…