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Random Fields For Spatial Data Modeling


Random Fields For Spatial Data Modeling
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Random Fields For Spatial Data Modeling


Random Fields For Spatial Data Modeling
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Author : Dionissios T. Hristopulos
language : en
Publisher: Springer Nature
Release Date : 2020-02-17

Random Fields For Spatial Data Modeling written by Dionissios T. Hristopulos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-17 with Science categories.


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.



Collecting Spatial Data


Collecting Spatial Data
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Author : Werner G. Müller
language : en
Publisher: Physica
Release Date : 1998-10-20

Collecting Spatial Data written by Werner G. Müller and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-20 with Business & Economics categories.


The book is concerned with the statistical theory for locating spatial sensors. It bridges the gap between spatial statistics and optimum design theory. After introductions to those two fields the topics of exploratory designs and designs for spatial trend and variogram estimation are treated. A new methodology, so-called approximate information matrices, are employed to cope with the problem of correlated observations. A great number of relevant references are collected and put into a common perspective. The theoretical investigations are accompanied by a practical example, the redesign of an Upper-Austrian air pollution monitoring network. The reader will find respective theory and recommendations on how to efficiently plan a specific purpose spatial monitoring network.



Markov Random Field Modeling In Image Analysis


Markov Random Field Modeling In Image Analysis
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Author : Stan Z. Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03

Markov Random Field Modeling In Image Analysis written by Stan Z. Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Computers categories.


Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.



Spatial Statistics And Modeling


Spatial Statistics And Modeling
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Author : Carlo Gaetan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-10

Spatial Statistics And Modeling written by Carlo Gaetan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-10 with Mathematics categories.


Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete. The most important statistical methods and their asymptotic properties are described, including estimation in geostatistics, autocorrelation and second-order statistics, maximum likelihood methods, approximate inference using the pseudo-likelihood or Monte-Carlo simulations, statistics for point processes and Bayesian hierarchical models. A chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs sampler, Metropolis-Hastings algorithms and exact simulation). A large number of real examples are studied with R, and each chapter ends with a set of theoretical and applied exercises. While a foundation in probability and mathematical statistics is assumed, three appendices introduce some necessary background. The book is accessible to senior undergraduate students with a solid math background and Ph.D. students in statistics. Furthermore, experienced statisticians and researchers in the above-mentioned fields will find the book valuable as a mathematically sound reference. This book is the English translation of Modélisation et Statistique Spatiales published by Springer in the series Mathématiques & Applications, a series established by Société de Mathématiques Appliquées et Industrielles (SMAI).



Gaussian Markov Random Fields


Gaussian Markov Random Fields
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Author : Havard Rue
language : en
Publisher: CRC Press
Release Date : 2005-02-18

Gaussian Markov Random Fields written by Havard Rue and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-18 with Mathematics categories.


Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie



Hierarchical Modeling And Analysis For Spatial Data


Hierarchical Modeling And Analysis For Spatial Data
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Author : Sudipto Banerjee
language : en
Publisher: CRC Press
Release Date : 2003-12-17

Hierarchical Modeling And Analysis For Spatial Data written by Sudipto Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-17 with Mathematics categories.


Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis,



Continuum Models And Discrete Systems


Continuum Models And Discrete Systems
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Author : François Willot
language : en
Publisher: Springer Nature
Release Date : 2024-09-23

Continuum Models And Discrete Systems written by François Willot and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.


The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.



Statistical Modeling Using Bayesian Latent Gaussian Models


Statistical Modeling Using Bayesian Latent Gaussian Models
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Author : Birgir Hrafnkelsson
language : en
Publisher: Springer Nature
Release Date : 2023-11-08

Statistical Modeling Using Bayesian Latent Gaussian Models written by Birgir Hrafnkelsson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.


This book focuses on the statistical modeling of geophysical and environmental data using Bayesian latent Gaussian models. The structure of these models is described in a thorough introductory chapter, which explains how to construct prior densities for the model parameters, how to infer the parameters using Bayesian computation, and how to use the models to make predictions. The remaining six chapters focus on the application of Bayesian latent Gaussian models to real examples in glaciology, hydrology, engineering seismology, seismology, meteorology and climatology. These examples include: spatial predictions of surface mass balance; the estimation of Antarctica’s contribution to sea-level rise; the estimation of rating curves for the projection of water level to discharge; ground motion models for strong motion; spatial modeling of earthquake magnitudes; weather forecasting based on numerical model forecasts; and extreme value analysis of precipitation on a high-dimensional grid. The book is aimed at graduate students and experts in statistics, geophysics, environmental sciences, engineering, and related fields.



Life Cycle Of Structures And Infrastructure Systems


Life Cycle Of Structures And Infrastructure Systems
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Author : Fabio Biondini
language : en
Publisher: CRC Press
Release Date : 2023-06-28

Life Cycle Of Structures And Infrastructure Systems written by Fabio Biondini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-28 with Technology & Engineering categories.


Life-Cycle of Structures and Infrastructure Systems collects the lectures and papers presented at IALCCE 2023 – The Eighth International Symposium on Life-Cycle Civil Engineering held at Politecnico di Milano, Milan, Italy, 2-6 July, 2023. This Open Access Book contains the full papers of 514 contributions, including the Fazlur R. Khan Plenary Lecture, nine Keynote Lectures, and 504 technical papers from 45 countries. The papers cover recent advances and cutting-edge research in the field of life-cycle civil engineering, including emerging concepts and innovative applications related to life-cycle design, assessment, inspection, monitoring, repair, maintenance, rehabilitation, and management of structures and infrastructure systems under uncertainty. Major topics covered include life-cycle safety, reliability, risk, resilience and sustainability, life-cycle damaging processes, life-cycle design and assessment, life-cycle inspection and monitoring, life-cycle maintenance and management, life-cycle performance of special structures, life-cycle cost of structures and infrastructure systems, and life-cycle-oriented computational tools, among others. This Open Access Book provides an up-to-date overview of the field of life-cycle civil engineering and significant contributions to the process of making more rational decisions to mitigate the life-cycle risk and improve the life-cycle reliability, resilience, and sustainability of structures and infrastructure systems exposed to multiple natural and human-made hazards in a changing climate. It will serve as a valuable reference to all concerned with life-cycle of civil engineering systems, including students, researchers, practicioners, consultants, contractors, decision makers, and representatives of managing bodies and public authorities from all branches of civil engineering.



Bayesian Statistical Modeling With Stan R And Python


Bayesian Statistical Modeling With Stan R And Python
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Author : Kentaro Matsuura
language : en
Publisher: Springer Nature
Release Date : 2023-01-24

Bayesian Statistical Modeling With Stan R And Python written by Kentaro Matsuura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-24 with Computers categories.


This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language. The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines. Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.