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The effect of redundancy on probability bounds
, 2009
"... Lower bounds on the probability of a union obtained by applying optimal bounds to subsets of events can provide excellent bounds. Comparisons are made with bounds obtained by linear programming and in the cases considered, the best bound is obtained with a subset that contains no redundant events co ..."
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Cited by 3 (0 self)
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Lower bounds on the probability of a union obtained by applying optimal bounds to subsets of events can provide excellent bounds. Comparisons are made with bounds obtained by linear programming and in the cases considered, the best bound is obtained with a subset that contains no redundant events
PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 2217 (2 self)
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Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges
Probability Bounds Analysis in Environmental Risk Assessment
 Applied Biomathematics, Setauket
, 2003
"... This document provides a detailed overview of probability bounds analysis. In the sections that follow, the conceptual background of the approach is briefly presented, followed by the mathematical derivation of probability bounds around parametric, nonparametric, empirical, and assumed or stipulate ..."
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Cited by 16 (1 self)
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This document provides a detailed overview of probability bounds analysis. In the sections that follow, the conceptual background of the approach is briefly presented, followed by the mathematical derivation of probability bounds around parametric, nonparametric, empirical, and assumed
Precise Propagation of Upper and Lower Probability Bounds in
, 2000
"... 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 assertions of a given knowledge base, automatically obtaining the ..."
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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 assertions of a given knowledge base, automatically obtaining
An Improved Probability Bound for the Approximate SLemma
"... The purpose of this note is to give a probability bound on symmetric matrices to improve an error bound in the Approximate SLemma used in establishing levels of conservatism results for approximate robust counterparts. ..."
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The purpose of this note is to give a probability bound on symmetric matrices to improve an error bound in the Approximate SLemma used in establishing levels of conservatism results for approximate robust counterparts.
Probability Bounds Analysis for Nonlinear Dynamic Process Models
, 2009
"... Dynamic process models frequently involve uncertain parameters and inputs. Propagating these uncertainties rigorously through a mathematical model to determine their effect on system states and outputs is a challenging problem. In this work, we describe a new approach, based on the use of Taylor mod ..."
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Cited by 2 (0 self)
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model methods, for the rigorous propagation of uncertainties through nonlinear systems of ordinary differential equations (ODEs). We concentrate on uncertainties whose distribution is not known precisely, but can be bounded by a probability box (pbox), and show how to use pboxes in the context
Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
"... ..."
Some Results on Generalized Coherence of Conditional Probability Bounds
 Proc. of The Third International Symposium on Imprecise Probabilities and their Applications (ISIPTA ’03
, 2003
"... Based on the coherence principle of de Finetti and a related notion of generalized coherence (gcoherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of gcoherence is equivalent to the "avoiding uniform loss" property for lower an ..."
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Based on the coherence principle of de Finetti and a related notion of generalized coherence (gcoherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of gcoherence is equivalent to the "avoiding uniform loss" property for lower
Divergence measures based on the Shannon entropy
 IEEE Transactions on Information theory
, 1991
"... AbstractA new class of informationtheoretic divergence measures based on the Shannon entropy is introduced. Unlike the wellknown Kullback divergences, the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved. More importantly, ..."
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Cited by 657 (0 self)
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, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The new measures are also well characterized by the properties of nonnegativity, finiteness
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