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Author: Emilio Porcu
Publisher: Springer Science & Business Media
ISBN: 3642170862
Category : Mathematics
Languages : en
Pages : 263
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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.
Author: Emilio Porcu
Publisher: Springer Science & Business Media
ISBN: 3642170862
Category : Mathematics
Languages : en
Pages : 263
Get Book Here
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.
Author: Fabian Guignard
Publisher: Springer Nature
ISBN: 3030952312
Category : Science
Languages : en
Pages : 170
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Book Description
The gathering and storage of data indexed in space and time are experiencing unprecedented growth, demanding for advanced and adapted tools to analyse them. This thesis deals with the exploration and modelling of complex high-frequency and non-stationary spatio-temporal data. It proposes an efficient framework in modelling with machine learning algorithms spatio-temporal fields measured on irregular monitoring networks, accounting for high dimensional input space and large data sets. The uncertainty quantification is enabled by specifying this framework with the extreme learning machine, a particular type of artificial neural network for which analytical results, variance estimation and confidence intervals are developed. Particular attention is also paid to a highly versatile exploratory data analysis tool based on information theory, the Fisher-Shannon analysis, which can be used to assess the complexity of distributional properties of temporal, spatial and spatio-temporal data sets. Examples of the proposed methodologies are concentrated on data from environmental sciences, with an emphasis on wind speed modelling in complex mountainous terrain and the resulting renewable energy assessment. The contributions of this thesis can find a large number of applications in several research domains where exploration, understanding, clustering, interpolation and forecasting of complex phenomena are of utmost importance.
Author: Dionissios T. Hristopulos
Publisher: Springer Nature
ISBN: 9402419187
Category : Science
Languages : en
Pages : 884
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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.
Author: Edwin J. Green
Publisher: Springer Nature
ISBN: 303060750X
Category : Science
Languages : en
Pages : 188
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Book Description
This book presents modern Bayesian analysis in a format that is accessible to researchers in the fields of ecology, wildlife biology, and natural resource management. Bayesian analysis has undergone a remarkable transformation since the early 1990s. Widespread adoption of Markov chain Monte Carlo techniques has made the Bayesian paradigm the viable alternative to classical statistical procedures for scientific inference. The Bayesian approach has a number of desirable qualities, three chief ones being: i) the mathematical procedure is always the same, allowing the analyst to concentrate on the scientific aspects of the problem; ii) historical information is readily used, when appropriate; and iii) hierarchical models are readily accommodated. This monograph contains numerous worked examples and the requisite computer programs. The latter are easily modified to meet new situations. A primer on probability distributions is also included because these form the basis of Bayesian inference. Researchers and graduate students in Ecology and Natural Resource Management will find this book a valuable reference.
Author: Vladas Pipiras
Publisher: Cambridge University Press
ISBN: 1108210198
Category : Mathematics
Languages : en
Pages : 693
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Book Description
This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.
Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1439819181
Category : Mathematics
Languages : en
Pages : 583
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Book Description
Keep Up to Date with the Evolving Landscape of Space and Space-Time Data Analysis and ModelingSince the publication of the first edition, the statistical landscape has substantially changed for analyzing space and space-time data. More than twice the size of its predecessor, Hierarchical Modeling and Analysis for Spatial Data, Second Edition reflec
Author: Marco A. R. Ferreira
Publisher: CRC Press
ISBN: 1040217214
Category : Mathematics
Languages : en
Pages : 293
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Book Description
Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Modeling Spatio-Temporal Data: Markov Random Fields, Objectives Bayes, and Multiscale Models aims to fill this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets, including proper Gaussian Markov random fields, dynamic multiscale spatio-temporal models, and objective priors for spatial and spatio-temporal models. The goal is to make these approaches more accessible to practitioners, and to stimulate additional research in these important areas of spatial and spatio-temporal statistics. Key topics: Proper Gaussian Markov random fields and their uses as building blocks for spatio-temporal models and multiscale models. Hierarchical models with intrinsic conditional autoregressive priors for spatial random effects, including reference priors, results on fast computations, and objective Bayes model selection. Objective priors for state-space models and a new approximate reference prior for a spatio-temporal model with dynamic spatio-temporal random effects. Spatio-temporal models based on proper Gaussian Markov random fields for Poisson observations. Dynamic multiscale spatio-temporal thresholding for spatial clustering and data compression. Multiscale spatio-temporal assimilation of computer model output and monitoring station data. Dynamic multiscale heteroscedastic multivariate spatio-temporal models. The M-open multiple optima paradox and some of its practical implications for multiscale modeling. Ensembles of dynamic multiscale spatio-temporal models for smooth spatio-temporal processes. The audience for this book are practitioners, researchers, and graduate students in statistics, data science, machine learning, and related fields. Prerequisites for this book are master's-level courses on statistical inference, linear models, and Bayesian statistics. This book can be used as a textbook for a special topics course on spatial and spatio-temporal statistics, as well as supplementary material for graduate courses on spatial and spatio-temporal modeling.
Author: Dipak K. Dey
Publisher: CRC Press
ISBN: 1498701310
Category : Mathematics
Languages : en
Pages : 538
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Book Description
Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subje
Author: Anatoliy Malyarenko
Publisher: Cambridge University Press
ISBN: 1108429858
Category : Mathematics
Languages : en
Pages : 313
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Book Description
Presents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.
Author: Emilio Porcu
Publisher: Springer Science & Business Media
ISBN: 3642170854
Category : Mathematics
Languages : en
Pages : 263
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Book Description
This book arises from the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place March 2010. It details recent developments, new methods and applications in spatial statistics and related areas. This book arises from the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place March 2010. It details recent developments, new methods and applications in spatial statistics and related areas.
