Browsing by Author "Wilson, Kevin J."

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    Approximate uncertainty modeling in risk analysis with vine copulas
    (Wiley, 2015-09-02) Bedford, Tim; Daneshkhah, Alireza; Wilson, Kevin J.
    Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions that do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The article provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas that have such good levels of approximation. We extend previous approaches using vines by considering nonconstant conditional dependencies, which are particularly relevant in financial risk modeling. We discuss how such models may be quantified, in terms of expert judgment or by fitting data, and illustrate the approach by modeling two financial data sets.
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    Assessing parameter uncertainty on coupled models using minimum information methods
    (Elsevier Science B.V., Amsterdam., 2014-05-31T00:00:00Z) Bedford, Tim; Wilson, Kevin J.; Daneshkhah, Alireza
    Probabilistic inversion is used to take expert uncertainty assessments about observable model outputs and build from them a distribution on the model parameters that captures the uncertainty expressed by the experts. In this paper we look at ways to use minimum information methods to do this, focussing in particular on the problem of ensuring consistency between expert assessments about differing variables, either as outputs from a single model, or potentially as outputs along a chain of models. The paper shows how such a problem can be structured and then illustrates the method with two examples; one involving failure rates of equipment in series systems and the other atmospheric dispersion and deposition.