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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.
Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes. An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds ...
A contrasting example of this conception of the working hypothesis is illustrated by the brain-in-a-vat thought experiment. This experiment involves confronting the global skeptic position that we, in fact, are all just brains in vats being stimulated by a mad scientist to believe that our reality is real.
In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. [2] For the following definitions, two examples will be used. The first is the problem of character recognition given an array of bits encoding a binary-valued image. The other example is the problem of finding an interval that will ...
The observed data are statistically compared against the equivalence bounds. If the statistical test indicates the observed data is surprising, assuming that true effects are at least as extreme as the equivalence bounds, a Neyman-Pearson approach to statistical inferences can be used to reject effect sizes larger than the equivalence bounds ...
The probability density function (PDF) for the Wilson score interval, plus PDF s at interval bounds. Tail areas are equal. Since the interval is derived by solving from the normal approximation to the binomial, the Wilson score interval ( , + ) has the property of being guaranteed to obtain the same result as the equivalent z-test or chi-squared test.
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.
A research proposal is a document proposing a research project, generally in the sciences or academia, and generally constitutes a request for sponsorship of that research. [1] Proposals are evaluated on the cost and potential impact of the proposed research, and on the soundness of the proposed plan for carrying it out. [2] Research proposals ...