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This book gives a comprehensive view of non-linear geostatistics, from the first work by G. Matheron and A. Maréchal in the 1970s, to the latest developments related to geometric problems. The course notes, which form the first part of the book, correspond to the course on non-linear geostatistics for the CFSG, a postgraduate program in geostatistics offered by the Centre de Géostatique de Fontainebleau (École des Mines de Paris). In the second part of the book, three case-studies illustrate the subject.

Kriging --- Kriging. --- Basic Sciences. Statistics --- Applied Statistics --- Geology --- Mine valuation --- Nonlinear theories --- Statistical methods --- Applied Statistics.

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Geology. Earth sciences --- Mathematical statistics --- Geology --- Kriging --- Statistical methods --- Geology - Statistical methods

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"Spatial functional data (SFD) arises when we have functional data (curves or images) at each one of the several sites or areas of a region. Statistics for SFD is concerned with the application of methods for modeling this type of data. All the fields of spatial statistics (point patterns, areal data and geostatistics) have been adapted to the study of SFD. For example, in point patterns analysis, the functional mark correlation function is proposed as a counterpart of the mark correlation function; in areal data, analysis of a functional areal dataset consisting of population pyramids for 38 neighborhoods in Barcelona (Spain) has been proposed; and in geostatistical analysis diverse approaches for kriging of functional data have been given. In the last few years, some alternatives have been adapted for considering models for SFD, where the estimation of the spatial correlation is of interest. When a functional variable is measured in sites of a region, i.e. when there is a realisation of a functional random field (spatial functional stochastic process), it is important to test for significant spatial autocorrelation and study this correlation if present. Assessing whether SFD are or are not spatially correlated allows us to properly formulate a functional model. However, searching in the literature, it is clear that amongst the several categories of spatial functional methods, functional geostatistics has been much more developed considering both new methodological approaches and analysis of a wide range of case studies covering a wealth of varied fields of applications"--

Geology --- Géostatistique --- Kriging. --- Spatial analysis (Statistics) --- Analyse spatiale (statistique) --- Functional analysis. --- Analyse fonctionnelle --- Statistical methods. --- Géostatistique

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Coastal ecosystems are dynamic, complex, and often fragile transition environments between land and oceans. They are exclusive habitats for a broad range of living organisms, functioning as havens for biodiversity and providing several important ecological services that link terrestrial, freshwater, and marine environments. Humans living in coastal zones have been strongly dependent on these ecosystems as a source of food, physical protection against storms and advancing sea, and a range of human activities that generate economic income. Notwithstanding, the intensification of human activities in coastal areas of the recent decades, as well as the global climatic changes and coastal erosion processes of the present, have had detrimental impacts on these environments. Maintaining the structural and functional integrity of these environments and recovering an ecological balance or mitigating disturbances in systems under the influence of such stressors are complex tasks, only possible through the implementation of monitoring programs and by assessing their environmental quality. In this book, distinct approaches to environmental quality monitoring and assessment of coastal environments are presented, focused on abiotic and biotic compartments, and using tools that range from ecological levels of organization to the sub-organismal and the ecosystem levels.

Research & information: general --- Environmental economics --- radioactive materials --- trace metals --- bioaccumulation --- marine fish --- crustaceans --- marine environmental pollution --- Bay of Bengal --- beach litter --- infrared thermography --- UAV --- UGV --- environmental monitoring --- coastal pollution --- fuzzy modelling --- marine sediment --- Takagi–Sugeno --- ordinary kriging (OK) --- inverse distance weighting (IDW) --- spatial predictions --- endocrine disruptors --- Mugil cephalus --- PFNA --- ecosystem services --- benefit transfer --- meta-analysis --- meta-regression function

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Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging.

Stochastic processes --- Kriging. --- Geografie --- Topografie --- Geometric Modelling. --- Probabilities. --- Statistics . --- Geology. --- Geography. --- Earth sciences. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Geography, general. --- Earth Sciences, general. --- Geosciences --- Environmental sciences --- Physical sciences --- Cosmography --- Earth sciences --- World history --- Geognosy --- Geoscience --- Natural history --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk