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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.
The bounds may also be the tightest possible such bounds on the distribution function given the available information about it, in which case the bounds are therefore said to be best-possible. It may commonly be the case, however, that not every distribution that lies within these bounds is a possible distribution for the uncertain number, even ...
Therefore, space is a condition of possibility because it is a necessary condition for the existence of cubes to be possible. Note, however, that space did not cause the cube, but that the artisan did, and that the cube and space are distinct entities, so space is not part of the definition of cube.
In a graphical representation of the continuous uniform distribution function [()], the area under the curve within the specified bounds, displaying the probability, is a rectangle. For the specific example above, the base would be 16 , {\displaystyle 16,} and the height would be 1 23 . {\displaystyle {\tfrac {1}{23}}.} [ 5 ]
Tshilidzi Marwala and Evan Hurwitz in their study on bounded rationality observed that advances in technology (e.g. computer processing power because of Moore's law, artificial intelligence, and big data analytics) expand the bounds that define the feasible rationality space. Because of this expansion of the bounds of rationality, machine ...
Uncertainty is traditionally modelled by a probability distribution, as developed by Kolmogorov, [1] Laplace, de Finetti, [2] Ramsey, Cox, Lindley, and many others.However, this has not been unanimously accepted by scientists, statisticians, and probabilists: it has been argued that some modification or broadening of probability theory is required, because one may not always be able to provide ...
The intuition behind the CDF-based approach is that bounds on the CDF of a distribution can be translated into bounds on statistical functionals of that distribution. Given an upper and lower bound on the CDF, the approach involves finding the CDFs within the bounds that maximize and minimize the statistical functional of interest.
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively.