ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Approximate Uncertainty Modelling with Vine Copulas

13 September 2016, 10:30 – 10:50

Abstract

Submitted by
Kevin Wilson
Authors
Kevin Wilson (Newcastle University), Tim Bedford (University of Strathclyde), Alireza Daneshkhah (Cranfield University)
Abstract
Many applications require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modelling joint uncertainties with probability distributions. This talk 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 which do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. We discuss a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. This result is further operationalised by showing how minimum information copulas can be used to provide parametric classes of copulas which have such good levels of approximation. We extend previous approaches using vines by considering non-constant conditional dependencies which are particularly relevant in financial risk modelling. We discuss how such models may be quantified, in terms of expert judgement or by fitting data, and illustrate the approach by modelling two financial data and component lifetimes.

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