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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 that the 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.".
- Probability_bounds_analysis wikiPageExternalLink intprob.
- Probability_bounds_analysis wikiPageExternalLink pbawhite.pdf.
- Probability_bounds_analysis wikiPageExternalLink epistemic.
- Probability_bounds_analysis wikiPageExternalLink www.sipta.org.
- Probability_bounds_analysis wikiPageID "34450103".
- Probability_bounds_analysis wikiPageRevisionID "580748616".
- Probability_bounds_analysis ''b''_ "−∞".
- Probability_bounds_analysis ''p''_ "∞".
- Probability_bounds_analysis hasPhotoCollection Probability_bounds_analysis.
- 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 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".
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- Probability_bounds_analysis sameAs Q7246873.
- Probability_bounds_analysis sameAs Q7246873.
- Probability_bounds_analysis wasDerivedFrom Probability_bounds_analysis?oldid=580748616.
- Probability_bounds_analysis isPrimaryTopicOf Probability_bounds_analysis.