Probabilistic arithmetic

By R. Williamson. 1989

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Citations in the corpus

Consistent Kernel Mean Estimation for Functions of Random Variables (2016, background): “For real valued distributions, integral transforms (Springer, 1979), mixtures of Gaussians (Milios, 2009), Laguerre polynomials (Williamson, 1989), and Chebyshev polynomials (Korzeń and Jaroszewicz, 2014) were proposed as convenient representations for numerical computation.”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “[49] proposes an approximation using Laguerre polynomials, and a notion of envelopes bounding the cumulative distribution function.”
Constructing Probability Boxes and Dempster-Shafer Structures (2003, background): “This approach seems to consider the imprecision present in such problems to be primarily about the probabilities, rather than the x-values (contra Williamson 1989).”
Bounds for joint portfolios of dependent risks (2012, background): “The following typically strong improvements of the risk bounds of the joint portfolio under the additional positive dependence restrictions have been given in several similar forms in the literature; see Williamson and Downs (1990); Embrechts et al. (2003); [Rü] (2005); [EP] (2006b).”
Imprecise probabilities in engineering analyses (2013, unknown): “This problem is part of a more general problem of modeling stochastic and functional dependency in any probabilistic arithmetic for which probability bounds analysis was originally created to address [185, 163].”
Setting the Operating Reserve Using Probabilistic Wind Power Forecasts (2011, methodology): “Assuming independence, the sum can be computed by convolution [32]:”
Arithmetic Operations on Independent Random Variables: A Numerical Approach (2012, methodology): “chapters of [22] (and works by other authors) use so-called envelopes, that is, upper and lower bounds on the cumulative distribution functions (c.”
Dependence in Dempster-Shafer theory and probability bounds analysis* (2004, background): “Dependency bounds analysis (Makarov 1981; Frank et al. 1987; Williamson 1989; Williamson and Downs 1990; Ferson and Long 1995) produces such bounds, which are often also mathematically best possible in the sense of being as tight as possible given the stated information.”