{"product_id":"uncertainty-analysis-with-high-dimensional-dependence-modelling-9780470863060","title":"Uncertainty Analysis with High Dimensional","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMathematical 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…an invaluable reference for researchers, practitioners and graduate students in several areas of statistics, engineering and technology.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2007b)  \u003cp\u003e\"...whether one is a researcher, student, or an industrial practitioner dealing with computer models the book comes highly recommended.\" (\u003ci\u003eTechnometrics\u003c\/i\u003e, February 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Wags and Bogsats 1\u003c\/p\u003e \u003cp\u003e1.2 Uncertainty analysis and decision support: a recent example 4\u003c\/p\u003e \u003cp\u003e1.3 Outline of the book 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Assessing Uncertainty on Model Input 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 13\u003c\/p\u003e \u003cp\u003e2.2 Structured expert judgment in outline 14\u003c\/p\u003e \u003cp\u003e2.3 Assessing distributions of continuous univariate uncertain quantities 15\u003c\/p\u003e \u003cp\u003e2.4 Assessing dependencies 16\u003c\/p\u003e \u003cp\u003e2.5 Unicorn 20\u003c\/p\u003e \u003cp\u003e2.6 Unicorn projects 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Bivariate Dependence 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 25\u003c\/p\u003e \u003cp\u003e3.2 Measures of dependence 26\u003c\/p\u003e \u003cp\u003e3.2.1 Product moment correlation 26\u003c\/p\u003e \u003cp\u003e3.2.2 Rank correlation 30\u003c\/p\u003e \u003cp\u003e3.2.3 Kendall’s tau 32\u003c\/p\u003e \u003cp\u003e3.3 Partial, conditional and multiple correlations 32\u003c\/p\u003e \u003cp\u003e3.4 Copulae 34\u003c\/p\u003e \u003cp\u003e3.4.1 Fréchet copula 36\u003c\/p\u003e \u003cp\u003e3.4.2 Diagonal band copula 37\u003c\/p\u003e \u003cp\u003e3.4.3 Generalized diagonal band copula 41\u003c\/p\u003e \u003cp\u003e3.4.4 Elliptical copula 42\u003c\/p\u003e \u003cp\u003e3.4.5 Archimedean copulae 45\u003c\/p\u003e \u003cp\u003e3.4.6 Minimum information copula 47\u003c\/p\u003e \u003cp\u003e3.4.7 Comparison of copulae 49\u003c\/p\u003e \u003cp\u003e3.5 Bivariate normal distribution 50\u003c\/p\u003e \u003cp\u003e3.5.1 Basic properties 50\u003c\/p\u003e \u003cp\u003e3.6 Multivariate extensions 51\u003c\/p\u003e \u003cp\u003e3.6.1 Multivariate dependence measures 51\u003c\/p\u003e \u003cp\u003e3.6.2 Multivariate copulae 53\u003c\/p\u003e \u003cp\u003e3.6.3 Multivariate normal distribution 53\u003c\/p\u003e \u003cp\u003e3.7 Conclusions 54\u003c\/p\u003e \u003cp\u003e3.8 Unicorn projects 55\u003c\/p\u003e \u003cp\u003e3.9 Exercises 61\u003c\/p\u003e \u003cp\u003e3.10 Supplement 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 High-dimensional Dependence Modelling 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 81\u003c\/p\u003e \u003cp\u003e4.2 Joint normal transform 82\u003c\/p\u003e \u003cp\u003e4.3 Dependence trees 86\u003c\/p\u003e \u003cp\u003e4.3.1 Trees 86\u003c\/p\u003e \u003cp\u003e4.3.2 Dependence trees with copulae 86\u003c\/p\u003e \u003cp\u003e4.3.3 Example: Investment 90\u003c\/p\u003e \u003cp\u003e4.4 Dependence vines 92\u003c\/p\u003e \u003cp\u003e4.4.1 Vines 92\u003c\/p\u003e \u003cp\u003e4.4.2 Bivariate- and copula-vine specifications 96\u003c\/p\u003e \u003cp\u003e4.4.3 Example: Investment continued 98\u003c\/p\u003e \u003cp\u003e4.4.4 Partial correlation vines 99\u003c\/p\u003e \u003cp\u003e4.4.5 Normal vines 101\u003c\/p\u003e \u003cp\u003e4.4.6 Relationship between conditional rank and partial correlations on a regular vine 101\u003c\/p\u003e \u003cp\u003e4.5 Vines and positive definiteness 105\u003c\/p\u003e \u003cp\u003e4.5.1 Checking positive definiteness 105\u003c\/p\u003e \u003cp\u003e4.5.2 Repairing violations of positive definiteness 107\u003c\/p\u003e \u003cp\u003e4.5.3 The completion problem 109\u003c\/p\u003e \u003cp\u003e4.6 Conclusions 111\u003c\/p\u003e \u003cp\u003e4.7 Unicorn projects 111\u003c\/p\u003e \u003cp\u003e4.8 Exercises 115\u003c\/p\u003e \u003cp\u003e4.9 Supplement 116\u003c\/p\u003e \u003cp\u003e4.9.1 Proofs 116\u003c\/p\u003e \u003cp\u003e4.9.2 Results for Section 4.4.6 127\u003c\/p\u003e \u003cp\u003e4.9.3 Example of fourvariate correlation matrices 129\u003c\/p\u003e \u003cp\u003e4.9.4 Results for Section 4.5.2 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Other Graphical Models 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 131\u003c\/p\u003e \u003cp\u003e5.2 Bayesian belief nets 131\u003c\/p\u003e \u003cp\u003e5.2.1 Discrete bbn’s 132\u003c\/p\u003e \u003cp\u003e5.2.2 Continuous bbn’s 133\u003c\/p\u003e \u003cp\u003e5.3 Independence graphs 141\u003c\/p\u003e \u003cp\u003e5.4 Model inference 142\u003c\/p\u003e \u003cp\u003e5.4.1 Inference for bbn’s 143\u003c\/p\u003e \u003cp\u003e5.4.2 Inference for independence graphs 144\u003c\/p\u003e \u003cp\u003e5.4.3 Inference for vines 145\u003c\/p\u003e \u003cp\u003e5.5 Conclusions 150\u003c\/p\u003e \u003cp\u003e5.6 Unicorn projects 150\u003c\/p\u003e \u003cp\u003e5.7 Supplement 157\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Sampling Methods 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 159\u003c\/p\u003e \u003cp\u003e6.2 (Pseudo-) random sampling 160\u003c\/p\u003e \u003cp\u003e6.3 Reduced variance sampling 161\u003c\/p\u003e \u003cp\u003e6.3.1 Quasi-random sampling 161\u003c\/p\u003e \u003cp\u003e6.3.2 Stratified sampling 164\u003c\/p\u003e \u003cp\u003e6.3.3 Latin hypercube sampling 166\u003c\/p\u003e \u003cp\u003e6.4 Sampling trees, vines and continuous bbn’s 168\u003c\/p\u003e \u003cp\u003e6.4.1 Sampling a tree 168\u003c\/p\u003e \u003cp\u003e6.4.2 Sampling a regular vine 169\u003c\/p\u003e \u003cp\u003e6.4.3 Density approach to sampling regular vine 174\u003c\/p\u003e \u003cp\u003e6.4.4 Sampling a continuous bbn 174\u003c\/p\u003e \u003cp\u003e6.5 Conclusions 180\u003c\/p\u003e \u003cp\u003e6.6 Unicorn projects 180\u003c\/p\u003e \u003cp\u003e6.7 Exercise 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Visualization 185\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 185\u003c\/p\u003e \u003cp\u003e7.2 A simple problem 186\u003c\/p\u003e \u003cp\u003e7.3 Tornado graphs 186\u003c\/p\u003e \u003cp\u003e7.4 Radar graphs 187\u003c\/p\u003e \u003cp\u003e7.5 Scatter plots, matrix and overlay scatter plots 188\u003c\/p\u003e \u003cp\u003e7.6 Cobweb plots 191\u003c\/p\u003e \u003cp\u003e7.7 Cobweb plots local sensitivity: dike ring reliability 195\u003c\/p\u003e \u003cp\u003e7.8 Radar plots for importance; internal dosimetry 199\u003c\/p\u003e \u003cp\u003e7.9 Conclusions 201\u003c\/p\u003e \u003cp\u003e7.10 Unicorn projects 201\u003c\/p\u003e \u003cp\u003e7.11 Exercises 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Probabilistic Sensitivity Measures 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 205\u003c\/p\u003e \u003cp\u003e8.2 Screening techniques 205\u003c\/p\u003e \u003cp\u003e8.2.1 Morris’ method 205\u003c\/p\u003e \u003cp\u003e8.2.2 Design of experiments 208\u003c\/p\u003e \u003cp\u003e8.3 Global sensitivity measures 214\u003c\/p\u003e \u003cp\u003e8.3.1 Correlation ratio 215\u003c\/p\u003e \u003cp\u003e8.3.2 Sobol indices 219\u003c\/p\u003e \u003cp\u003e8.4 Local sensitivity measures 222\u003c\/p\u003e \u003cp\u003e8.4.1 First order reliability method 222\u003c\/p\u003e \u003cp\u003e8.4.2 Local probabilistic sensitivity measure 223\u003c\/p\u003e \u003cp\u003e8.4.3 Computing ∂E(X|g o) ∂ go 225\u003c\/p\u003e \u003cp\u003e8.5 Conclusions 227\u003c\/p\u003e \u003cp\u003e8.6 Unicorn projects 228\u003c\/p\u003e \u003cp\u003e8.7 Exercises 230\u003c\/p\u003e \u003cp\u003e8.8 Supplement 236\u003c\/p\u003e \u003cp\u003e8.8.1 Proofs 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Probabilistic Inversion 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 239\u003c\/p\u003e \u003cp\u003e9.2 Existing algorithms for probabilistic inversion 240\u003c\/p\u003e \u003cp\u003e9.2.1 Conditional sampling 240\u003c\/p\u003e \u003cp\u003e9.2.2 Parfum 242\u003c\/p\u003e \u003cp\u003e9.2.3 Hora-Young and PREJUDICE algorithms 243\u003c\/p\u003e \u003cp\u003e9.3 Iterative algorithms 243\u003c\/p\u003e \u003cp\u003e9.3.1 Iterative proportional fitting 244\u003c\/p\u003e \u003cp\u003e9.3.2 Iterative PARFUM 245\u003c\/p\u003e \u003cp\u003e9.4 Sample re-weighting 246\u003c\/p\u003e \u003cp\u003e9.4.1 Notation 246\u003c\/p\u003e \u003cp\u003e9.4.2 Optimization approaches 247\u003c\/p\u003e \u003cp\u003e9.4.3 IPF and PARFUM for sample re-weighting probabilistic inversion 248\u003c\/p\u003e \u003cp\u003e9.5 Applications 249\u003c\/p\u003e \u003cp\u003e9.5.1 Dispersion coefficients 249\u003c\/p\u003e \u003cp\u003e9.5.2 Chicken processing line 252\u003c\/p\u003e \u003cp\u003e9.6 Convolution constraints with prescribed margins 253\u003c\/p\u003e \u003cp\u003e9.7 Conclusions 255\u003c\/p\u003e \u003cp\u003e9.8 Unicorn projects 256\u003c\/p\u003e \u003cp\u003e9.9 Supplement 258\u003c\/p\u003e \u003cp\u003e9.9.1 Proofs 258\u003c\/p\u003e \u003cp\u003e9.9.2 IPF and PARFUM 263\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Uncertainty and the UN Compensation Commission 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 269\u003c\/p\u003e \u003cp\u003e10.2 Claims based on uncertainty 270\u003c\/p\u003e \u003cp\u003e10.3 Who pays for uncertainty 272\u003c\/p\u003e \u003cp\u003eBibliography 273\u003c\/p\u003e \u003cp\u003eIndex 281\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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