Uncertainty Analysis with High Dimensional Dependence Modelling

Abstract

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. 3.3 Partial, conditional and multiple correlations. 3.4 Copulae. 3.5 Bivariate normal distribution. 3.6 Multivariate extensions. 3.7 Conclusions. 3.8 Unicorn projects. 3.9 Exercises. 3.10 Supplement. 4 High-dimensional Dependence Modelling. 4.1 Introduction. 4.2 Joint normal transform. 4.3 Dependence trees. 4.4 Dependence vines. 4.5 Vines and positive definiteness. 4.6 Conclusions. 4.7 Unicorn projects. 4.8 Exercises. 4.9 Supplement. 5 Other Graphical Models. 5.1 Introduction. 5.2 Bayesian belief nets. 5.3 Independence graphs. 5.4 Model inference. 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. 6.4 Sampling trees, vines and continuous bbn's. 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. 7.10 Unicorn projects. 7.11 Exercises. 8 Probabilistic Sensitivity Measures. 8.1 Introduction. 8.2 Screening techniques. 8.3 Global sensitivity measures. 8.4 Local sensitivity measures. 8.5 Conclusions. 8.6 Unicorn projects. 8.7 Exercises. 8.8 Supplement . 8.8.1 Proofs. 9 Probabilistic Inversion. 9.1 Introduction. 9.2 Existing algorithms for probabilistic inversion. 9.2.1 Conditional sampling. 9.3 Iterative algorithms. 9.4 Sample re-weighting. 9.5 Applications. 9.6 Convolution constraints with prescribed margins. 9.7 Conclusions. 9.8 Unicorn projects. 9.9 Supplement. 10 Uncertainty and the UN Compensation Commission. 10.1 Introduction. 10.2 Claims based on uncertainty. 10.3 Who pays for uncertainty. Bibliography. Index.