05473nam 22006254a 450 991083002290332120230829000918.01-280-64995-X97866106499520-470-86307-20-470-86308-0(CKB)1000000000356051(EBL)274402(SSID)ssj0000263915(PQKBManifestationID)11192364(PQKBTitleCode)TC0000263915(PQKBWorkID)10283144(PQKB)11168849(MiAaPQ)EBC274402(OCoLC)85820898(EXLCZ)99100000000035605120051116d2006 uy 0engur|n|---|||||txtccrUncertainty analysis with high dimensional dependence modelling[electronic resource] /Dorota Kurowicka and Roger CookeChichester, England ;Hoboken, NJ Wileyc20061 online resource (308 p.)Wiley series in probability and statisticsDescription based upon print version of record.0-470-86306-4 Includes bibliographical references (p. [273]-279) and index.Uncertainty Analysis with High Dimensional Dependence Modelling; Contents; Preface; 1 Introduction; 1.1 Wags and Bogsats; 1.2 Uncertainty analysis and decision support: a recent example; 1.3 Outline of the book; 2 Assessing Uncertainty on Model Input; 2.1 Introduction; 2.2 Structured expert judgment in outline; 2.3 Assessing distributions of continuous univariate uncertain quantities; 2.4 Assessing dependencies; 2.5 Unicorn; 2.6 Unicorn projects; 3 Bivariate Dependence; 3.1 Introduction; 3.2 Measures of dependence; 3.2.1 Product moment correlation; 3.2.2 Rank correlation; 3.2.3 Kendall's tau3.3 Partial, conditional and multiple correlations3.4 Copulae; 3.4.1 Fr ́echet copula; 3.4.2 Diagonal band copula; 3.4.3 Generalized diagonal band copula; 3.4.4 Elliptical copula; 3.4.5 Archimedean copulae; 3.4.6 Minimum information copula; 3.4.7 Comparison of copulae; 3.5 Bivariate normal distribution; 3.5.1 Basic properties; 3.6 Multivariate extensions; 3.6.1 Multivariate dependence measures; 3.6.2 Multivariate copulae; 3.6.3 Multivariate normal distribution; 3.7 Conclusions; 3.8 Unicorn projects; 3.9 Exercises; 3.10 Supplement; 4 High-dimensional Dependence Modelling; 4.1 Introduction4.2 Joint normal transform4.3 Dependence trees; 4.3.1 Trees; 4.3.2 Dependence trees with copulae; 4.3.3 Example: Investment; 4.4 Dependence vines; 4.4.1 Vines; 4.4.2 Bivariate- and copula-vine specifications; 4.4.3 Example: Investment continued; 4.4.4 Partial correlation vines; 4.4.5 Normal vines; 4.4.6 Relationship between conditional rank and partial correlations on a regular vine; 4.5 Vines and positive definiteness; 4.5.1 Checking positive definiteness; 4.5.2 Repairing violations of positive definiteness; 4.5.3 The completion problem; 4.6 Conclusions; 4.7 Unicorn projects; 4.8 Exercises4.9 Supplement4.9.1 Proofs; 4.9.2 Results for Section 4.4.6; 4.9.3 Example of fourvariate correlation matrices; 4.9.4 Results for Section 4.5.2; 5 Other Graphical Models; 5.1 Introduction; 5.2 Bayesian belief nets; 5.2.1 Discrete bbn's; 5.2.2 Continuous bbn's; 5.3 Independence graphs; 5.4 Model inference; 5.4.1 Inference for bbn's; 5.4.2 Inference for independence graphs; 5.4.3 Inference for vines; 5.5 Conclusions; 5.6 Unicorn projects; 5.7 Supplement; 6 Sampling Methods; 6.1 Introduction; 6.2 (Pseudo-) random sampling; 6.3 Reduced variance sampling; 6.3.1 Quasi-random sampling6.3.2 Stratified sampling6.3.3 Latin hypercube sampling; 6.4 Sampling trees, vines and continuous bbn's; 6.4.1 Sampling a tree; 6.4.2 Sampling a regular vine; 6.4.3 Density approach to sampling regular vine; 6.4.4 Sampling a continuous bbn; 6.5 Conclusions; 6.6 Unicorn projects; 6.7 Exercise; 7 Visualization; 7.1 Introduction; 7.2 A simple problem; 7.3 Tornado graphs; 7.4 Radar graphs; 7.5 Scatter plots, matrix and overlay scatter plots; 7.6 Cobweb plots; 7.7 Cobweb plots local sensitivity: dike ring reliability; 7.8 Radar plots for importance; internal dosimetry; 7.9 Conclusions7.10 Unicorn projectsMathematical 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 tWiley series in probability and statistics.Uncertainty (Information theory)MathematicsUncertainty (Information theory)Mathematics.003.54003/.54Kurowicka Dorota1967-474601Cooke Roger1942-731611MiAaPQMiAaPQMiAaPQBOOK9910830022903321Uncertainty analysis with high dimensional dependence modelling1441399UNINA