Uncertainty analysis with high dimensional dependence modellingMathematical models are used to simulate complex real-world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty. Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model-based decision-making. In recent years there has been an explosion of interest in uncertainty analysis. Uncertainty and dependence elicitation, dependence modelling, model inference, efficient sampling, screening and sensitivity analysis, and probabilistic inversion are among the active research areas. This text provides both the mathematical foundations and practical applications in this rapidly expanding area, including:
Uncertainty Analysis with High Dimensional Dependence Modelling offers a comprehensive exploration of a new emerging field. It will prove an invaluable text for researches, practitioners and graduate students in areas ranging from statistics and engineering to reliability and environmetrics. |
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Contents
Assessing Uncertainty on Model Input | 13 |
Bivariate Dependence | 25 |
Highdimensional Dependence Modelling | 81 |
Copyright | |
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Common terms and phrases
Applied assessed Bayesian bbn's bivariate bulb calculate Chapter cobweb plot coefficients columns compute conditional correlations conditional distribution conditional expectation conditional independence conditional rank correlations conditionally independent conditioned set constraints Cooke correlation matrix correlation ratio crew alertness cumulative distribution function D-vine Data denote density dependence structure diagonal band copula edges elliptical copula equal example expert judgment Figure Frank's copula graphical headlite Hence high-dimensional ign-head ignitn independence graph Inference iterative joint distribution joint normal distribution Kendall's tau Kurowicka Lemma linear marginal distributions measure method minimal Multivariate nodes output parameters PARFUM algorithm partial correlation percentile positive definite probabilistic inversion problem product moment correlation Proof Proposition quantiles random variables random vector rank correlation matrix re-weighting Regression regular vine relative information sampling procedure scatter plots Second Edition shows simulation specified Statistical strtr Theorem tree uncertainty analysis UNICORN uniform distribution values variance zero