Uncertainty Analysis with High Dimensional Dependence Modelling

Dorota Kurowicka, Delft University of Technology, The Netherlands.Roger M. Cooke, Delft University of Technology, The Netherlands.

• Preface ix1 Introduction 11.1 Wags and Bogsats 11.2 Uncertainty analysis and decision support: a recent example 41.3 Outline of the book 92 Assessing Uncertainty on Model Input 132.1 Introduction 132.2 Structured expert judgment in outline 142.3 Assessing distributions of continuous univariate uncertain quantities 152.4 Assessing dependencies 162.5 Unicorn 202.6 Unicorn projects 203 Bivariate Dependence 253.1 Introduction 253.2 Measures of dependence 263.3 Partial, conditional and multiple correlations 323.4 Copulae 343.5 Bivariate normal distribution 503.6 Multivariate extensions 513.7 Conclusions 543.8 Unicorn projects 553.9 Exercises 613.10 Supplement 674 High-dimensional Dependence Modelling 814.1 Introduction 814.2 Joint normal transform 824.3 Dependence trees 864.4 Dependence vines 924.5 Vines and positive definiteness 1054.6 Conclusions 1114.7 Unicorn projects 1114.8 Exercises 1154.9 Supplement 1165 Other Graphical Models 1315.1 Introduction 1315.2 Bayesian belief nets 1315.3 Independence graphs 1415.4 Model inference 1425.5 Conclusions 1505.6 Unicorn projects 1505.7 Supplement 1576 Sampling Methods 1596.1 Introduction 1596.2 (Pseudo-) random sampling 1606.3 Reduced variance sampling 1616.4 Sampling trees, vines and continuous bbn’s 1686.5 Conclusions 1806.6 Unicorn projects 1806.7 Exercise 1847 Visualization 1857.1 Introduction 1857.2 A simple problem 1867.3 Tornado graphs 1867.4 Radar graphs 1877.5 Scatter plots, matrix and overlay scatter plots 1887.6 Cobweb plots 1917.7 Cobweb plots local sensitivity: dike ring reliability 1957.8 Radar plots for importance; internal dosimetry 1997.9 Conclusions 2017.10 Unicorn projects 2017.11 Exercises 2038 Probabilistic Sensitivity Measures 2058.1 Introduction 2058.2 Screening techniques 2058.3 Global sensitivity measures 2148.4 Local sensitivity measures 2228.5 Conclusions 2278.6 Unicorn projects 2288.7 Exercises 2308.8 Supplement 2369 Probabilistic Inversion 2399.1 Introduction 2399.2 Existing algorithms for probabilistic inversion 2409.3 Iterative algorithms 2439.4 Sample re-weighting 2469.5 Applications 2499.6 Convolution constraints with prescribed margins 2539.7 Conclusions 2559.8 Unicorn projects 2569.9 Supplement 25810 Uncertainty and the UN Compensation Commission 26910.1 Introduction 26910.2 Claims based on uncertainty 27010.3 Who pays for uncertainty 272Bibliography 273Index 281

"…an invaluable reference for researchers, practitioners and graduate students in several areas of statistics, engineering and technology." (Mathematical Reviews, 2007b) "...whether one is a researcher, student, or an industrial practitioner dealing with computer models the book comes highly recommended." (Technometrics, February 2007)