Constructing Probability Boxes and Dempster-Shafer Structures

By Scott Ferson, Vladik Kreinovick, Lev Ginzburg, Fari Sentz. 2003

763 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Signal Processing

View Paper: https://www.semanticscholar.org/paper/8eff743341521cca30f6d2a48df50bf6977c96b2

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In Artificial Intelligence

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Citations in the corpus

Imprecise probabilities in engineering analyses (2013, neutral): “Probability bounds analysis [162, 163, 164, 61] is another of the uncertainty quanti cation approaches that are considered part of the theory of imprecise probability [44].”
Sensitivity in risk analyses with uncertain numbers. (2006, methodology): “We call such calculations “probability bounds analysis” (PBA) (Ferson 1994; 2002; Ferson et al. 2003).”
Validation of imprecise probability models (2009, methodology): “…that methods beyond traditional probability theory might be necessary for models that must distinguish aleatory and epistemic uncertainty (Shafer 1976; Walley 1991; Klir and Wierman 1999; Oberkampf et al. 2001; Nikolaidis and Haftka 2001; Ferson et al. 2003; Helton and Oberkampf 2004; inter alia).”
Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model (2013, background): “, fuzzy set theory [8], DempsterShafer theory of evidence [9]-[14], possibility the ory [15]-[18] and interval analysis [19]-[21].”
Interval Monte Carlo methods for structural reliability (2010, methodology): “In [6,9], probability boxes and Dempster-Shafer structures were used to bound imprecisely specified probability distributions.”
n-MONOTONE EXACT FUNCTIONALS (2008, background): “…called credal sets; see Levi [13]), and they provide a unifying framework for studying many other uncertainty models, such as probability charges (Bhaskara Rao and Bhaskara Rao [3]), 2- andn-monotone set functions (Choquet [4]), possibility measures ([5, 6, 7, 11]), and p-boxes (Fersonet al. [12]).”
Aleatoric and epistemic uncertainty in groundwater flow and transport simulation (2009, background): “If the intervals used to construct the random sets are certain to contain the value of the measured variable, the true (and unknown) probability distribution, which the confidence intervals aim to characterize, defining a random variable lies between the plausibility and belief curves, especially wh”
Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory (2018, background): “A probability box or simply p-box is the set of CDFs {FX : FX(x) ≤ FX(x) ≤ FX(x), x ∈ R} which conjointly represents the uncertainty about the true CDF associated to a random variable X (Ferson et al., 2003).”
Experimental uncertainty estimation and statistics for data having interval uncertainty. (2007, background): “Several recent papers have explored this idea and have started developing formulas and algorithms necessary to compute basic statistics for interval data* (e.g., Ferson et al. 2002a,b; 2005; Wu et al. 2003; Kreinovich, et al. 2005b,c; Gioia and Lauro 2005; Xiang et al. 2006).”
Machine Learning for High-entropy Alloys: Progress, Challenges and Opportunities (2022, methodology): “Except for DS evidence theory, there are also many other UQ methods, including fuzzy sets [216], interval methods [217], and information theory [218], as well as probabilistic approaches such as Bayesian methods [219] and probability boxes [220].”