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Spatiotemporal Random Fields

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Spatiotemporal Random Fields

Spatiotemporal Random Fields Book
Author : George Christakos
Publisher : Elsevier
Release : 2017-07-26
ISBN : 0128030321
Language : En, Es, Fr & De

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Book Description :

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. Contains applications in the form of examples and case studies, providing readers with first-hand experiences Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Random Field Models in Earth Sciences

Random Field Models in Earth Sciences Book
Author : George Christakos
Publisher : Courier Corporation
Release : 2012-08-09
ISBN : 0486160912
Language : En, Es, Fr & De

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Book Description :

This text for graduate students examines problems related to earth and environmental sciences by means of theoretical models based on a purely random (stochastic) element. 103 figures. 16 tables.

Modern Spatiotemporal Geostatistics

Modern Spatiotemporal Geostatistics Book
Author : George Christakos
Publisher : Oxford University Press
Release : 2000-11-30
ISBN : 0198031793
Language : En, Es, Fr & De

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Book Description :

It is widely recognized that the techniques of classical geostatistics, which have been used for several decades, have reached their limit, and the time has come for some alternative approaches to be given a chance. This book, therefore, is an introduction to the fundamentals of modern geostatistics, which is a group of spatiotemporal concepts and methods that are the products of the advancement of the epistemic status of stochastic data analysis. The latter is considered from a novel perspective, promoting the view that a deeper understanding of a theory of knowledge is an important prerequisite for the development of improved mathematical models of scientific mapping. The main focus of the book is the Bayesian Maximum Entropy (BME) approach for studying spatiotemporal distributions of natural variables. As part of the modern geostatistics paradigm, the BME approach provides a fundamental insight into the mapping problem in which the knowledge of a natural variable, not the variable itself, is the direct object of study. The thread running throughout the book is that the modern geostatistical approach to environmental problems is that of natural scientists who are more interested in a stochastic analysis concerned with both the ontological level(building models for physical systems) and the epistemic level (using what we know about the physical systems and integrating and modeling knowledge from a variety of scientific disciplines), rather than in the pure naive inductive account of science based merely on a linear relationship between data and hypotheses and theory-free techniques that may be useful in other areas.

Random Field Models in Earth Sciences

Random Field Models in Earth Sciences Book
Author : George Christakos
Publisher : Elsevier
Release : 2013-10-22
ISBN : 1483288307
Language : En, Es, Fr & De

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Book Description :

This book is about modeling as a prinicipal component of scientific investigations. In general terms, modeling is the funamental process of combining intellectual creativity with physical knowledge and mathematical techniques in order to learn the properties of the mechanisms underlying a physical phenomenon and make predictions. The book focuses on a specific class of models, namely, random field models and certain of their physical applications in the context of a stochastic data analysis and processing research program. The term application is considered here in the sense wherein the mathematical random field model is shaping, but is also being shaped by, its objects. Key Features * This book explores the application of random field models and stochastic data processing to problems in hydrogeology, geostatistics, climate modeling, and oil reservoir engineering, among others Researchers in the geosciences who work with models of natural processes will find discussion of; * Spatiotemporal random fields * Space transformation * Multidimensional estimation * Simulation * Sampling design * Stochastic partial differential equations

Control of Spatially Structured Random Processes and Random Fields with Applications

Control of Spatially Structured Random Processes and Random Fields with Applications Book
Author : Ruslan K. Chornei,Hans Daduna,Pavel S. Knopov
Publisher : Springer Science & Business Media
Release : 2006-09-03
ISBN : 038731279X
Language : En, Es, Fr & De

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Book Description :

This book is devoted to the study and optimization of spatiotemporal stochastic processes - processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems. The book presents problems and content not considered in other books on controlled Markov processes, especially regarding controlled Markov fields on graphs.

Spatiotemporal Random Fields

Spatiotemporal Random Fields Book
Author : George Christakos
Publisher : Unknown
Release : 2017-07-26
ISBN : 9780128030127
Language : En, Es, Fr & De

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Book Description :

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. Contains applications in the form of examples and case studies, providing readers with first-hand experiences Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Random Fields for Spatial Data Modeling

Random Fields for Spatial Data Modeling Book
Author : Dionissios T. Hristopulos
Publisher : Springer Nature
Release : 2020-02-17
ISBN : 9402419187
Language : En, Es, Fr & De

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Book Description :

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Spatiotemporal Environmental Health Modelling A Tractatus Stochasticus

Spatiotemporal Environmental Health Modelling  A Tractatus Stochasticus Book
Author : George Christakos,Dionissios Hristopulos
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 1475728115
Language : En, Es, Fr & De

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Book Description :

Spatiotemporal Environmental Health Modelling: A Tractatus Stochasticus provides a holistic, conceptual and quantitative framework for Environmental Health Modelling in space-time. The holistic framework integrates two aspects of Environmental Health Science that have been previously treated separately: the environmental aspect, which involves the natural processes that bring about human exposure to harmful substances; and the health aspect, which focuses on the interactions of these substances with the human body. Some of the fundamental issues addressed in this work include variability, scale, uncertainty, and space-time connectivity. These topics are important in the characterization of natural systems and health processes. Spatiotemporal Environmental Health Modelling: A Tractatus Stochasticus explains why modern stochastics is the appropriate mechanical vehicle for addressing such issues in a rigorous way. In particular, modern stochastics incorporates concepts and methods from probability, classical statistics, geostatistics, statistical mechanics and field theory. The authors present a synthetic view of environmental health that embraces all of the various components and focuses on their mutual interactions. Spatiotemporal Environmental Health Modeling: A Tractatus Stochasticus includes new material on Bayesian maximum entropy estimation techniques and space-time random field estimation methods. The authors show why these methods have clear advantages over the classical geostatistical estimation procedures and how they can be used to provide accurate space-time maps of environmental health processes. Also included are expositions of diagrammatic perturbation and renormalization group analysis, which have not been previously discussed within the context of Environmental Health. Finally, the authors present stochastic indicators that can be used for large-scale characterization of contamination and investigations of health effects at the microscopic level. This book will be a useful reference to both researchers and practitioners of Environmental Health Sciences. It will appeal specifically to environmental engineers, geographers, geostatisticians, earth scientists, toxicologists, epidemiologists, pharmacologists, applied mathematicians, physicists and biologists.

Probabilistic and Stochastic Methods in Analysis with Applications

Probabilistic and Stochastic Methods in Analysis  with Applications Book
Author : J.S. Byrnes,Kathryn A. Hargreaves,Karl Berry
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401127913
Language : En, Es, Fr & De

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Book Description :

Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

Spatio temporal Design

Spatio temporal Design Book
Author : Jorge Mateu,Werner G. Müller
Publisher : John Wiley & Sons
Release : 2012-11-05
ISBN : 1118441885
Language : En, Es, Fr & De

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Book Description :

A state-of-the-art presentation of optimum spatio-temporalsampling design - bridging classic ideas with modern statisticalmodeling concepts and the latest computational methods. Spatio-temporal Design presents a comprehensivestate-of-the-art presentation combining both classical and moderntreatments of network design and planning for spatial andspatio-temporal data acquisition. A common problem set isinterwoven throughout the chapters, providing various perspectivesto illustrate a complete insight to the problem at hand. Motivated by the high demand for statistical analysis of datathat takes spatial and spatio-temporal information into account,this book incorporates ideas from the areas of time series, spatialstatistics and stochastic processes, and combines them to discussoptimum spatio-temporal sampling design. Spatio-temporal Design: Advances in Efficient DataAcquisition: Provides an up-to-date account of how to collect space-timedata for monitoring, with a focus on statistical aspects and thelatest computational methods Discusses basic methods and distinguishes between design andmodel-based approaches to collecting space-time data. Features model-based frequentist design for univariate andmultivariate geostatistics, and second-phase spatial sampling. Integrates common data examples and case studies throughout thebook in order to demonstrate the different approaches and theirintegration. Includes real data sets, data generating mechanisms andsimulation scenarios. Accompanied by a supporting website featuring R code. Spatio-temporal Design presents an excellent book forgraduate level students as well as a valuable reference forresearchers and practitioners in the fields of applied mathematics,engineering, and the environmental and health sciences.

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA Book
Author : Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue
Publisher : CRC Press
Release : 2018-12-07
ISBN : 0429629850
Language : En, Es, Fr & De

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Book Description :

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Spatiotemporal Analysis of Extreme Hydrological Events

Spatiotemporal Analysis of Extreme Hydrological Events Book
Author : Gerald Corzo,Emmanouil Varouchakis
Publisher : Elsevier
Release : 2018-11-20
ISBN : 0128117311
Language : En, Es, Fr & De

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Book Description :

Spatio-temporal Analysis of Extreme Hydrological Events offers an extensive view of the experiences and applications of the latest developments and methodologies for analyzing and understanding extreme environmental and hydrological events. The book addresses the topic using spatio-temporal methods, such as space-time geostatistics, machine learning, statistical theory, hydrological modelling, neural network and evolutionary algorithms. This important resource for both hydrologists and statisticians interested in the framework of spatial and temporal analysis of hydrological events will provide users with an enhanced understanding of the relationship between magnitude, dynamics and the probability of extreme hydrological events. Presents spatio-temporal processes, including multivariate dynamic modelling Provides varying methodological approaches, giving the readers multiple hydrological modelling information to use in their work Includes a variety of case studies making the context of the book relatable to everyday working situations

Quantitative Analysis and Modeling of Earth and Environmental Data

Quantitative Analysis and Modeling of Earth and Environmental Data Book
Author : Jiaping Wu,Junyu He,George Christakos
Publisher : Elsevier
Release : 2021-12-04
ISBN : 0128163429
Language : En, Es, Fr & De

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Book Description :

Quantitative Analysis and Modeling of Earth and Environmental Data: Space-Time and Spacetime Data Considerations introduces the notion of chronotopologic data analysis that offers a systematic, quantitative analysis of multi-sourced data and provides information about the spatial distribution and temporal dynamics of natural attributes (physical, biological, health, social). It includes models and techniques for handling data that may vary by space and/or time, and aims to improve understanding of the physical laws of change underlying the available numerical datasets, while taking into consideration the in-situ uncertainties and relevant measurement errors (conceptual, technical, computational). It considers the synthesis of scientific theory-based methods (stochastic modeling, modern geostatistics) and data-driven techniques (machine learning, artificial neural networks) so that their individual strengths are combined by acting symbiotically and complementing each other. The notions and methods presented in Quantitative Analysis and Modeling of Earth and Environmental Data: Space-Time and Spacetime Data Considerations cover a wide range of data in various forms and sources, including hard measurements, soft observations, secondary information and auxiliary variables (ground-level measurements, satellite observations, scientific instruments and records, protocols and surveys, empirical models and charts). Including real-world practical applications as well as practice exercises, this book is a comprehensive step-by-step tutorial of theory-based and data-driven techniques that will help students and researchers master data analysis and modeling in earth and environmental sciences (including environmental health and human exposure applications). Explores the analysis and processing of chronotopologic (i.e., space-time and spacetime) data that varies spatially and/or temporally, which is the case with the majority of data in scientific and engineering disciplines Studies the synthesis of scientific theory and empirical evidence (in its various forms) that offers a mathematically rigorous and physically meaningful assessment of real-world phenomena Covers a wide range of data describing a variety of attributes characterizing physical phenomena and systems including earth, ocean and atmospheric variables, environmental and ecological parameters, population health states, disease indicators, and social and economic characteristics Includes case studies and practice exercises at the end of each chapter for both real-world applications and deeper understanding of the concepts presented

Integrative Problem Solving in a Time of Decadence

Integrative Problem Solving in a Time of Decadence Book
Author : George Christakos
Publisher : Springer Science & Business Media
Release : 2010-12-10
ISBN : 9048198909
Language : En, Es, Fr & De

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Book Description :

Presents a unique study of Integrative Problem-Solving (IPS). The consideration of 'Decadence' is essential in the scientific study of environmental and other problems and their rigorous solution, because the broad context within which the problems emerge can affect their solution. Stochastic reasoning underlines the conceptual and methodological framework of IPS, and its formulation has a mathematical life of its own that accounts for the multidisciplinarity of real world problems, the multisourced uncertainties characterizing their solution, and the different thinking modes of the people involved. Only by interpolating between the full range of disciplines (including stochastic mathematics, physical science, neuropsychology, philosophy, and sociology) and the associated thinking modes can scientists arrive at a satisfactory account of problem-solving, and be able to distinguish between a technically complete problem-solution, and a solution that has social impact.

Advances in Contemporary Statistics and Econometrics

Advances in Contemporary Statistics and Econometrics Book
Author : Abdelaati Daouia,Anne Ruiz-Gazen
Publisher : Springer Nature
Release : 2021-06-14
ISBN : 3030732495
Language : En, Es, Fr & De

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Book Description :

This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.

Spatio Temporal Statistics with R

Spatio Temporal Statistics with R Book
Author : Christopher K. Wikle,Andrew Zammit-Mangion,Noel Cressie
Publisher : CRC Press
Release : 2019-02-18
ISBN : 0429649789
Language : En, Es, Fr & De

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Book Description :

The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.

Advances and Challenges in Space time Modelling of Natural Events

Advances and Challenges in Space time Modelling of Natural Events Book
Author : Emilio Porcu,José–María Montero,Martin Schlather
Publisher : Springer Science & Business Media
Release : 2012-01-05
ISBN : 3642170862
Language : En, Es, Fr & De

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Book Description :

This book arises as the natural continuation of the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place in Toledo (Spain) in March 2010. This Spring School above all focused on young researchers (Master students, PhD students and post-doctoral researchers) in academics, extra-university research and the industry who are interested in learning about recent developments, new methods and applications in spatial statistics and related areas, and in exchanging ideas and findings with colleagues.

Progress in Spatial Analysis

Progress in Spatial Analysis Book
Author : Antonio Páez,Julie Gallo,Ron N. Buliung,Sandy Dall'erba
Publisher : Springer Science & Business Media
Release : 2009-10-30
ISBN : 9783642033261
Language : En, Es, Fr & De

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Book Description :

Space is increasingly recognized as a legitimate factor that influences many processes and conceptual frameworks, including notions of spatial coherence and spatial heterogeneity that have been demonstrated to provide substance to both theory and explanation. The potential and relevance of spatial analysis is increasingly understood by an expanding sphere of cogent disciplines that have adopted the tools of spatial analysis. This book brings together major new developments in spatial analysis techniques, including spatial statistics, econometrics, and spatial visualization, and applications to fields such as regional studies, transportation and land use, political and economic geography, population and health. Establishing connections to existing and emerging lines of research, the book also serves as a survey of the field of spatial analysis and its links with related areas.

Computational Science ICCS 2008

Computational Science     ICCS 2008 Book
Author : Marian Bubak,Geert Dick van Albada,Jack Dongarra,Peter M.A. Sloot
Publisher : Springer Science & Business Media
Release : 2008-06-11
ISBN : 3540693866
Language : En, Es, Fr & De

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Book Description :

– Martin Walker:NewParadigmsforComputationalScience – Yong Shi:MultipleCriteriaMathematicalProgrammingandDataMining – Hank Childs: Why Petascale Visualization and Analysis Will Change the Rules – Fabrizio Gagliardi:HPCOpportunitiesandChallengesine-Science – Pawel Gepner:Intel'sTechnologyVisionandProductsforHPC – Jarek Nieplocha:IntegratedDataandTaskManagementforScienti?c- plications – Neil F. Johnson:WhatDoFinancialMarkets,WorldofWarcraft,andthe War in Iraq, all Have in Common? Computational Insights into Human CrowdDynamics We would like to thank all keynote speakers for their interesting and inspiring talks and for submitting the abstracts and papers for these proceedings. Fig. 1. Number of papers in the general track by topic The main track of ICSS 2008 was divided into approximately 20 parallel sessions (see Fig. 1) addressing the following topics: 1. e-Science Applications and Systems 2. Scheduling and Load Balancing 3. Software Services and Tools Preface VII 4. New Hardware and Its Applications 5. Computer Networks 6. Simulation of Complex Systems 7. Image Processing and Visualization 8. Optimization Techniques 9. Numerical Linear Algebra 10. Numerical Algorithms # papers 25 23 19 20 17 14 14 15 10 10 10 10 9 10 8 8 8 7 5 0 Fig. 2. Number of papers in workshops The conference included the following workshops (Fig. 2): 1. 7th Workshop on Computer Graphics and Geometric Modeling 2. 5th Workshop on Simulation of Multiphysics Multiscale Systems 3. 3rd Workshop on Computational Chemistry and Its Applications 4. Workshop on Computational Finance and Business Intelligence 5. Workshop on Physical, Biological and Social Networks 6. Workshop on GeoComputation 7. 2nd Workshop on Teaching Computational Science 8.