1. Forward -- 2. Preface -- 3. Introduction -- 4. Part I. Chapter 1 Kriging, Splines, Conditional Simulation, Bayesian In-version and Ensemble Kalman Filtering -- 5. Chapter 2 A Statistical Commentary on Mineral Prospectivity analysis -- 6. Chapter 3 Testing joint conditional independence of categorical random variables with a standard log-likelihood ratio test -- 7. Chapter 4 Modelling Compositional Data. The Sample Space Approach -- 8. Chapter 5 Properties of Sums of Geological Random Variables -- 9. Chapter 6 A Statistical Analysis of the Jacobian in Retrievals of Satellite Data -- 10. Chapter 7 All Realizations All the Time -- 11. Chapter 8 Binary Coefficients Redux -- 12. Chapter 9 Tracking Plurigaussian Simulations -- 13. Chapter 10 Mathematical Geosciences: Local Singularity Analysis of Nonlinear Earth Processes and Extreme Geo-Events -- 14. Chapter 11 Electrofacies in Reservoir Characterization -- 15. Chapter 12 Forecast of Shoreline Variations by Means of Median Sets -- 16. Chapter 13 An Introduction to the Spatio-Temporal Analysis of Sat-ellite Remote Sensing Data for Geostatisticians -- 17. Chapter 14 Flint drinking water crisis: a first attempt to model geo-statistically the space-time distribution of water lead levels -- 18. Chapter 15 Statistical Parametric Mapping for Geoscience Applications -- 19. Chapter 16 Water chemistry: are new challenges possible from CoDA (Compositional Data Analysis) point of view? -- 20. Chapter 17 Analysis of the United States Portion of the North American Soil Geochemical Landscapes Project – A Compositional Framework Approach -- 21. Chapter 18 Quantifying the Impacts of Uncertainty -- 22. Chapter 19. Advances in Sensitivity Analysis of Uncertainty due to Sampling Density for Spatially Correlated Attributes -- 23. Chapter 20 Predicting Molybdenum Deposit Growth -- 24. Chapter 21 General Framework of Quantitative Target Selections -- 25. Chapter 22 Solving the Wrong Resource Assessment Problems Precisely -- 26. Chapter 23 two ideas for analysis of multivariate geochemical survey data: proximity regression and principal component residuals -- 27. Chapter 24 Mathematical minerals: A history of petrophysical petrography -- 28. Chapter 25 Geostatistics for Seismic Characterization of Oil Reservoirs -- 29. Chapter 26 Statistical Modeling of Regional and Worldwide Size-Frequency Distributions of Metal Deposits -- 30. Chapter 27 Bayesianism in the Geosciences -- 31.Chapter 28 Geological Objects and Physical Parameter Fields in the Subsurface: A Review -- 32.Chapter 29 Fifty Years of Kriging -- 33. Chapter 30 Multiple Point Statistics: A Review -- 34. Chapter 31 When Should We Use Multiple-Point Geostatistics? -- 35. Chapter 32 The Origins of the Multiple-Point Statistics (MPS) Algorithm -- 36. Chapter 33 Predictive Geometallurgy: An Interdisciplinary Key Challenge for Mathematical Geosciences? -- 37. Chapter 34 Data Science for Geoscience: Leveraging Mathematical Geosciences with Semantics and Open Data -- 38. Chapter 35 Mathematical Morphology in Geosciences and GISci: An Illustrative Review -- 39. Chapter 36 IAMG: Recollections from the Early Years -- 40. Chapter 37 Forward and Inverse Models over 70 Years -- 41. Chapter 38 From individual personal contacts 1962–1968 to my 50 years of service -- 42. Chapter 39 Andrey Borisovich Vistelius -- 43. Chapter 40 Fifty Years’ Experience with Hidden Errors in Applying Classic Mathematical Geology -- 44. Chapter 41 Mathematical Geology by Example: Teaching and Learning Perspectives. .

Open Access

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.