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• Probability_bounds_analysis abstract "Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs. Such bounds are called probability boxes, and constrain cumulative probability distributions (rather than densities or mass functions).This bounding approach permits analysts to make calculations without requiring overly precise assumptions about parameter values, dependence among variables, or even distribution shape. Probability bounds analysis is essentially a combination of the methods of standard interval analysis and classical probability theory. Probability bounds analysis gives the same answer as interval analysis does when only range information is available. It also gives the same answers as Monte Carlo simulation does when information is abundant enough to precisely specify input distributions and their dependencies. Thus, it is a generalization of both interval analysis and probability theory.The diverse methods comprising probability bounds analysis provide algorithms to evaluate mathematical expressions when there is uncertainty about the input values, their dependencies, or even the form of mathematical expression itself. The calculations yield results that are guaranteed to enclose all possible distributions of the output variable if the input p-boxes were also sure to enclose their respective distributions. In some cases, a calculated p-box will also be best-possible in the sense thatthe bounds could be no tighter without excluding some of the possibledistributions.P-boxes are usually merely bounds on possible distributions. The bounds often also enclose distributions that are not themselves possible. For instance, the set of probability distributions that could result from adding random values without the independence assumption from two (precise) distributions is generally a proper subset of all the distributions enclosed by the p-box computed for the sum. That is, there are distributions within the output p-box that could not arise under any dependence between the two input distributions. The output p-box will, however, always contain all distributions that are possible, so long as the input p-boxes were sure to enclose their respective underlying distributions. This property often suffices for use in risk analysis and other fields requiring calculations under uncertainty.".
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• Probability_bounds_analysis wikiPageExternalLink pbawhite.pdf.
• Probability_bounds_analysis wikiPageExternalLink epistemic.
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• Probability_bounds_analysis wikiPageWikiLink Boolean_function.
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• Probability_bounds_analysis wikiPageWikiLink Category:Probability_bounds_analysis.
• Probability_bounds_analysis wikiPageWikiLink Category:Risk_analysis.
• Probability_bounds_analysis wikiPageWikiLink Chebyshev.
• Probability_bounds_analysis wikiPageWikiLink Chebyshev_inequality.
• Probability_bounds_analysis wikiPageWikiLink Chebyshevs_inequality.
• Probability_bounds_analysis wikiPageWikiLink Comonotonicity.
• Probability_bounds_analysis wikiPageWikiLink Convolution.
• Probability_bounds_analysis wikiPageWikiLink Convolution_of_probability_distributions.
• Probability_bounds_analysis wikiPageWikiLink Copula_(probability_theory).
• Probability_bounds_analysis wikiPageWikiLink Countermonotonicity.
• Probability_bounds_analysis wikiPageWikiLink Cumulative_distribution_function.
• Probability_bounds_analysis wikiPageWikiLink Curse_of_dimensionality.
• Probability_bounds_analysis wikiPageWikiLink Distribution_function.
• Probability_bounds_analysis wikiPageWikiLink Expected_value.
• Probability_bounds_analysis wikiPageWikiLink Frechet_inequalities.
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• Probability_bounds_analysis wikiPageWikiLink Importance_sampling.
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• Probability_bounds_analysis wikiPageWikiLink Interval_(mathematics).
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• Probability_bounds_analysis wikiPageWikiLink Interval_arithmetic.
• Probability_bounds_analysis wikiPageWikiLink John_Maynard_Keynes.
• Probability_bounds_analysis wikiPageWikiLink Kolmogorov.
• Probability_bounds_analysis wikiPageWikiLink Latin_hypercube.
• Probability_bounds_analysis wikiPageWikiLink Latin_hypercube_sampling.
• Probability_bounds_analysis wikiPageWikiLink Logical_conjunction.
• Probability_bounds_analysis wikiPageWikiLink Logical_disjunction.
• Probability_bounds_analysis wikiPageWikiLink Markov_inequality.
• Probability_bounds_analysis wikiPageWikiLink Markovs_inequality.
• Probability_bounds_analysis wikiPageWikiLink Mathematical_optimization.
• Probability_bounds_analysis wikiPageWikiLink Mathematical_programming.
• Probability_bounds_analysis wikiPageWikiLink Maurice_René_Fréchet.
• Probability_bounds_analysis wikiPageWikiLink Monte_Carlo_method.
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• Probability_bounds_analysis wikiPageWikiLink NP-hard.
• Probability_bounds_analysis wikiPageWikiLink NP-hardness.
• Probability_bounds_analysis wikiPageWikiLink Naive_set_theory.
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• Probability_bounds_analysis wikiPageWikiLink P-box.
• Probability_bounds_analysis wikiPageWikiLink Pafnuty_Chebyshev.
• Probability_bounds_analysis wikiPageWikiLink Positive_quadrant_dependence.
• Probability_bounds_analysis wikiPageWikiLink Probabilistic_risk_assessment.
• Probability_bounds_analysis wikiPageWikiLink Probability_box.
• Probability_bounds_analysis wikiPageWikiLink Probability_density_function.
• Probability_bounds_analysis wikiPageWikiLink Probability_mass_function.
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• Probability_bounds_analysis wikiPageWikiLink Real_number.
• Probability_bounds_analysis wikiPageWikiLink Risk_analysis.
• Probability_bounds_analysis wikiPageWikiLink Robust_Bayes_analysis.
• Probability_bounds_analysis wikiPageWikiLink Robust_Bayesian_analysis.
• Probability_bounds_analysis wikiPageWikiLink Second-order_Monte_Carlo_simulation.
• Probability_bounds_analysis wikiPageWikiLink Subset.
• Probability_bounds_analysis wikiPageWikiLink The_Laws_of_Thought.
• Probability_bounds_analysis wikiPageWikiLink Uncertainty_quantification.
• Probability_bounds_analysis wikiPageWikiLink Upper_and_lower_bounds.
• Probability_bounds_analysis wikiPageWikiLink Variance.
• Probability_bounds_analysis wikiPageWikiLink Verifiable_computing.
• Probability_bounds_analysis wikiPageWikiLink Verified_computing.
• Probability_bounds_analysis wikiPageWikiLinkText "Probability bounds analysis".
• Probability_bounds_analysis wikiPageWikiLinkText "probability bounds analysis".
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• Probability_bounds_analysis subject Category:Mathematical_analysis.
• Probability_bounds_analysis subject Category:Probability_bounds_analysis.
• Probability_bounds_analysis subject Category:Risk_analysis.
• Probability_bounds_analysis hypernym Collection.
• Probability_bounds_analysis type Book.
• Probability_bounds_analysis type Field.
• Probability_bounds_analysis type Concept.
• Probability_bounds_analysis comment "Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs.".
• Probability_bounds_analysis label "Probability bounds analysis".
• Probability_bounds_analysis sameAs m.0j46kks.
• Probability_bounds_analysis sameAs Q7246873.
• Probability_bounds_analysis sameAs Q7246873.
• Probability_bounds_analysis wasDerivedFrom Probability_bounds_analysis?oldid=670013120.

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