LEADER 05473nam 22006254a 450 001 9910830022903321 005 20230829000918.0 010 $a1-280-64995-X 010 $a9786610649952 010 $a0-470-86307-2 010 $a0-470-86308-0 035 $a(CKB)1000000000356051 035 $a(EBL)274402 035 $a(SSID)ssj0000263915 035 $a(PQKBManifestationID)11192364 035 $a(PQKBTitleCode)TC0000263915 035 $a(PQKBWorkID)10283144 035 $a(PQKB)11168849 035 $a(MiAaPQ)EBC274402 035 $a(OCoLC)85820898 035 $a(EXLCZ)991000000000356051 100 $a20051116d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aUncertainty analysis with high dimensional dependence modelling$b[electronic resource] /$fDorota Kurowicka and Roger Cooke 210 $aChichester, England ;$aHoboken, NJ $cWiley$dc2006 215 $a1 online resource (308 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-470-86306-4 320 $aIncludes bibliographical references (p. [273]-279) and index. 327 $aUncertainty 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 tau 327 $a3.3 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 Introduction 327 $a4.2 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 Exercises 327 $a4.9 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 sampling 327 $a6.3.2 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 Conclusions 327 $a7.10 Unicorn projects 330 $aMathematical models are used to simulate complex real-world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty. Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model-based decision-making. In recent years there has been an explosion of interest in uncertainty analysis. Uncertainty and dependence elicitation, dependence modelling, model inference, efficient sampling, screening and sensitivity analysis, and probabilistic inversion are among t 410 0$aWiley series in probability and statistics. 606 $aUncertainty (Information theory)$xMathematics 615 0$aUncertainty (Information theory)$xMathematics. 676 $a003.54 676 $a003/.54 700 $aKurowicka$b Dorota$f1967-$0474601 701 $aCooke$b Roger$f1942-$0731611 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830022903321 996 $aUncertainty analysis with high dimensional dependence modelling$91441399 997 $aUNINA