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ForewordPreface IntroductionB. S. Daya Sagar, Qiuming Cheng, Frits AgterbergPart I Theory1. Kriging, Splines, Conditional Simulation, Bayesian In-version and Ensemble Kalman Filtering                                                            Olivier Dubrule1.1 Introduction1.2 Deterministic Aspects of Geostatistics1.3 Stochastic Aspects of Geostatistics: Conditional Simulation1.4 Geostatistical Inversion of Seismic Data1.5 Kalman Filtering and Ensemble Kalman Filtering1.6 Beyond the Formal Relationship between Geostatistics and Bayes 1.7 ConclusionReferences2. A Statistical Commentary on Mineral Prospectivity analysis                                                                                            Adrian Baddeley2.1 Introduction2.2 Example Data2.3 Logistic Regression2.4 Poisson Point Process Models2.5 Monotone Regression2.6 Nonparametric Curve Estimation2.7 ROC curves2.8 Recursive PartitioningReferences3. Testing joint conditional independence of categorical random variables with a standard log-likelihood ratio test                                                                                 Helmut Schaeben3.1 Introduction3.2 From Contingency Tables to Log-Linear Models3.3 Independence, Conditional Independence of Random variables3.4 Logistic Regression, and its Special Case of Weightsof Evidence3.5 Hammersley-Clifford Theorem3.6 Testing Joint Conditional Independence of Categorical Random Variables3.7 Conditional Distribution, Logistic Regression3.8 Practical Applications3.9 Discussion and ConclusionsReferences4. Modelling Compositional Data. The Sample Space Ap-proach                                                                                                     Juan José Egozcue and Vera Pawlowsky-Glahn4.1 Introduction4.2 Scale Invariance, Key Principle of Compositions4.3 The Simplex as Sample Space of Compositions4.4 Perturbation, a Natural Shift Operation on Compositions4.5 Conditions on Metrics for Compositions4.6 Consequences of the Aitchison Geometry in the Sample Space of Compositional Data4.7 ConclusionsReferences5. Properties of Sums of Geological Random Variables                 G.M. Kaufman5.1 Introduction5.2 Preliminaries5.3 Thumbnail Case StudiesReferences6. A Statistical Analysis of the Jacobian in Retrievals of Satellite Data                                                                                               Noel Cressie6.1 Introduction6.2 A Statistical Framework for Satellite Retrievals6.3 The Jacobian Matrix and its Unit-Free Version6.4 Statistical Significance Filter6.5 ACOS Retrievals of the Atmospheric State from Japan’s GOSAT Satellite6.6 DiscussionReferences7. All Realizations All the Time                                                          Clayton V. Deutsch7.1 Introduction7.2 Simulation7.3 Decision Making7.4 Geostatistical Simulation7.5 Resource Decision Making7.6 Alternatives to All Realizations7.7 Concluding RemarksReferences8. Binary Coefficients Redux                                                               Michael E. Hohn8.1 Introduction8.2 Empirical Comparisons and a Taxonomy8.3 Effects of Rare and Endemic Taxa8.4 Adjusting for Poor Sampling 8.5 Metric? Euclidean?8.6 From Expected Values to Null Association8.7 Illustrative Example8.8 Discussion and Conclusions8.9 SummaryReferences9. Tracking Plurigaussian Simulations                                                          M. Armstrong, A. Mondaini and S. Camargo9.1 Introduction9.2 Review of Complex Networks9.3 Network Analysis of Google Citations of Plurigaus sian Simulations9.4 Diffusion of the New Method into Industry9.5 Conclusions and Perspectives for Future WorkReferences10. Mathematical Geosciences: Local Singularity Analysis of Nonlinear Earth Processes and Extreme Geo-Events Qiuming Cheng10.1 Introduction10.2 What is Mathematical Geosciences or Geomathemat ics?10.3 What contributions has MG made to geosciences?10.4 Frontiers of Earth science and opportunity of MG10.5 Fractal density and singularity analysis of nonlinear  geo-processes and extreme geo-events  10.6 Fractal Integral and fractal differential operations of nonlinear function10.7 Earth dynamics processes and extreme events10.8 Fractal density of continent rheology in phase transition zones and association with earthquakes 10.9 Discussion and Conclusions ReferencesPart II General Applications11. Electrofacies in Reservoir Characterization                                 John Davis11.1 Introduction11.2 The Amal Field of Libya11.3 Electrofacies Analysis11.4 What Do Amal Electrofacies Mean?11.5 ConclusionsReferences12. Forecast of Shoreline Variations by Means of Median Sets                                                                                           Jean Serra12.1 Three problems, One Theoretical Tool12.2 Median Set12.3 Median and Average for Non-Ordered Sets12.4 Extrapolations via the Quench Function12.5 Accretion and Homotopy12.6 ConclusionReferences13. An Introduction to the Spatio-Temporal Analysis of Sat-ellite Remote Sensing Data for Geostatisticians                                                                       A. F. Militino, M. D. Ugarte, and U. P´erez-Goya13.1 Introduction13.2 Satellite Images13.3 Derived Variables from Remote Sensing Data13.4 Pre-processing13.5 Spatial Interpolation13.6 Spatio-Temporal Interpolation13.7 ConclusionsReferences14. Flint drinking water crisis: a first attempt to model geo-statistically the space-time distribution of water lead levels                                                                                                        Pierre Goovaerts14.1 Introduction14.2 Materials and Methods14.3 Results and Discussion14.4 ConclusionsReferences15. Statistical Parametric Mapping for Geoscience Applica-tions                                                                                               Sean A. McKenna15.1 Introduction15.2 Anomaly Detection with Statistical Parametric Mapping15.3 Example Problems15.4 Summary References16. Water chemistry: are new challenges possible from CoDA (Compositional Data Analysis) point of view?                             Antonella Buccianti16.1 Water Chemistry Data as Compositional Data16.2 Isometric-Log Ratio Transformation: Is this the Key to Decipher the Dynamics of Geochemical Systems?16.3 Improving CoDA-Dendrogram: Checking for Vari ability, Resilience and Stability16.4 ConclusionsReferences17. Analysis of the United States Portion of the North Ameri-can Soil Geochemical Landscapes Project – A Composi-tional Framework Approach                                                                         E. C. Grunsky, L. J. Drew, and D. B. Smith17.1 Introduction17.2 Methods17.3 Results17.4 Discussion17.5 Concluding RemarksReferencesPart III Exploration and Resource Estimation18. Quantifying the Impacts of Uncertainty                                                 Peter Dowd18.1 Introduction18.2 Sources of In-Situ Uncertainty18.3 Transfer Uncertainty18.4 Consequences of In-Situ Uncertainty18.5 Quantifying Epistemic Uncertainty18.6 Quantifying the Effects of Transfer Uncertainty18.7 ConclusionReferences19. Advances in Sensitivity Analysis of Uncertainty due to Sampling Density for Spatially Correlated Attributes                                    Ricardo A. Olea19.1 Introduction19.2 Data19.3 Traditional Uncertainty Assessment19.4 Kriging19.5 Stochastic Simulation19.6 Validation19.7 ConclusionsReferences20. Predicting Molybdenum Deposit Growth                                              John H. Schuenemeyer, Lawrence J. Drew and James D. Bliss20.1 Introduction20.2 Cutoff Grade as a Function of Deposit Grade20.3 Deposit Growth as a Function of Cutoff Grade20.4  An Example20.5  ConclusionsReferences21. General Framework of Quantitative Target Selections Guocheng Pan21.1 Introduction21.2 Randomness of Mineral Endowment21.3 Fundamental Geo-Process Relations21.4 Scarceness, Rareness, and Exceptionalness21.5 Intrinsic Geological Unit21.6 Economic Truncation and Translation21.7 Information Synthesis21.8 Prediction with Dynamic Control SamplesReferences22. Solving the Wrong Resource Assessment Problems Pre-cisely                                                                                                 Donald A. Singer22.1 Introduction22.2 Target Population22.3 Examples of Mismatches in Assessments22.4 How to Correct Type III Errors22.5 ConclusionsReferences23. Two ideas for analysis of multivariate geochemical survey data: proximity regression and principal component re-siduals                                                                                                   G.F. Bonham-Carter and E. C. Grunsky23.1 Introduction23.2 Method 1: Direct Prediction of Spatial Proximity23.3 Method 2: Principal Component Residuals23.4 ConclusionsReferences24. Mathematical minerals: A history of petrophysical pe-trography                                                                                                   John H. Doveton24.1 Pioneering Computer Methods24.2 Mineralogy of Underdetermined Systems 24.3 Mineralogy of Overdetermined Systems24.4 Optimization Methods24.5 Clay Component Estimation 24.6 Normative Estimation by Geochemical Logs24.7 ConclusionReferences25. Geostatistics for Seismic Characterization of Oil Reser-voirs                                                                                                      Amílcar Soares and Leonado Azevedo25.1 Integration of Geophysical Data for Reservoir Modeling and Characterization25.2 Iterative Geostatistical Seismic Inversion Methodologies25.3 Trace-by-Trace Geostatistical Seismic Inversion 25.4 Global Geostatistical Seismic Inversion Methodologies25.5 Uncertainty and Risk Assessment at early stages of exploration25.6 Final RemarksReferences26. Statistical Modeling of Regional and Worldwide Size-Frequency Distributions of Metal Deposits                                            Frits Agterberg26.1 Introduction26.2 Modified Version of the Model of de Wijs Applied to Worldwide Metal Deposits26.3 Theory and Applications of the Pareto-Lognormal Model26.4 Upper Tail Pareto Distribution and its Connection to the Basic Lognormal Distribution26.5 Prediction of Future Copper Resources26.6 Concluding RemarksReferencesPart IV Reviews27. Bayesianism in the Geosciences                                                         Jef Caers27.1 Introduction27.2 A Historical P27.3 Science as Knowledge Derived from Facts, Data or Experience27.4 The Role of Experiments – Data 27.5 Induction vs Deduction27.6 Falsificationism27.7 Paradigms27.8 Bayesianism27.9 Bayesianism for Subsurface Systems27.10 SummaryReferences28. Geological Objects and Physical Parameter Fields in the Subsurface: A Review                                                                                 Guillaume Caumon28.1 Introduction28.2 Motivations for Explicit Geological Parameterizations28.3 Parameterizations for Physical Models28.4 Geological Parameterizations28.5 Conclusions and ChallengesReferences29. Fifty Years of Kriging                                                                           Jean-Paul Chilès and Nicolas Desassis29.1 Introduction29.2 The Origins of Kriging29.3 Development and Maturity: Trend, Neighborhood Selection29.4 Iterative Use of Kriging to Handle Inequality Data29.5 Nonstationary Covariance29.6 Kriging for Large Data Sets29.7 Iterative Algorithms for Solving the Kriging System29.8 ConclusionReferences30. Multiple Point Statistics: A Review&