Theory of Stochastic Objects

Theory of Stochastic Objects

This book defines and investigates the concept of a random object.

Author: Athanasios Christou Micheas

Publisher: CRC Press

ISBN: 9781466515222

Category: Mathematics

Page: 378

View: 688

This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete. Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics. Includes 378 exercises, with the solutions manual available on the book's website. 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example). The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.
Categories: Mathematics

Stochastic Processes

Stochastic Processes

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and ...

Author: Pierre Del Moral

Publisher: CRC Press

ISBN: 9781498701846

Category: Mathematics

Page: 866

View: 473

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
Categories: Mathematics

Stochastic Processes

Stochastic Processes

Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference.

Author: Peter Watts Jones

Publisher: CRC Press

ISBN: 9781498778121

Category: Mathematics

Page: 255

View: 252

Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues. The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference. This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.
Categories: Mathematics

Stationary Stochastic Processes

Stationary Stochastic Processes

Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial ...

Author: Georg Lindgren

Publisher: CRC Press

ISBN: 9781466557796

Category: Mathematics

Page: 375

View: 273

Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Categories: Mathematics

Modeling and Analysis of Stochastic Systems Third Edition

Modeling and Analysis of Stochastic Systems  Third Edition

Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models.

Author: Vidyadhar G. Kulkarni

Publisher: CRC Press

ISBN: 9781498756723

Category: Business & Economics

Page: 606

View: 871

Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.
Categories: Business & Economics

Theory and Modeling of Stochastic Objects

Theory and Modeling of Stochastic Objects

This book defines and investigates the concept of a random object.

Author: Athanasios Christou Micheas

Publisher: Chapman and Hall/CRC

ISBN: 1466515201

Category: Mathematics

Page: 416

View: 701

This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks. One would need to use one book on Real Analysis, one on Measure and/or Probability theory, one in Stochastic processes, and at least one on Statistics to capture the detail and depth of material that has gone into this text. The book is targeted towards students at the master's and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.
Categories: Mathematics

Stochastic Modeling of Scientific Data

Stochastic Modeling of Scientific Data

The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises.

Author: Peter Guttorp

Publisher: CRC Press

ISBN: 9781351413657

Category: Mathematics

Page: 384

View: 916

Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.
Categories: Mathematics

Modeling and Analysis of Stochastic Systems

Modeling and Analysis of Stochastic Systems

This practical text aims to enable students in engineering, business, operations research, public policy, and computer science to model and analyze stochastic systems.

Author: Vidyadhar G. Kulkarni

Publisher: CRC Press

ISBN: 0412049910

Category: Business & Economics

Page: 634

View: 380

This practical text aims to enable students in engineering, business, operations research, public policy, and computer science to model and analyze stochastic systems. The major classes of useful stochastic processes - discrete and continuous time Markov chains, renewal processes, regenerative processes, and Markov regenerative processes - are presented, with an emphasis on modelling real-life situations with stochastic elements and analyzing the resulting stochastic model.
Categories: Business & Economics

Operations Research and Management Science Handbook

Operations Research and Management Science Handbook

Basawa, I. V. and Prakasa Rao, B. L. S. (1980), Statistical Inference for Stochastic
Processes, Academic Press, New York. 6. Bhat, U. N. and Miller, G. K. ... of
Stochastic Systems. Texts in Statistical Science Series, Chapman & Hall, London.
25.

Author: A. Ravi Ravindran

Publisher: CRC Press

ISBN: 1420009710

Category: Technology & Engineering

Page: 904

View: 657

Operations Research (OR) began as an interdisciplinary activity to solve complex military problems during World War II. Utilizing principles from mathematics, engineering, business, computer science, economics, and statistics, OR has developed into a full fledged academic discipline with practical application in business, industry, government and military. Currently regarded as a body of established mathematical models and methods essential to solving complicated management issues, OR provides quantitative analysis of problems from which managers can make objective decisions. Operations Research and Management Science (OR/MS) methodologies continue to flourish in numerous decision making fields. Featuring a mix of international authors, Operations Research and Management Science Handbook combines OR/MS models, methods, and applications into one comprehensive, yet concise volume. The first resource to reach for when confronting OR/MS difficulties, this text – Provides a single source guide in OR/MS Bridges theory and practice Covers all topics relevant to OR/MS Offers a quick reference guide for students, researchers and practitioners Contains unified and up-to-date coverage designed and edited with non-experts in mind Discusses software availability for all OR/MS techniques Includes contributions from a mix of domestic and international experts The 26 chapters in the handbook are divided into two parts. Part I contains 14 chapters that cover the fundamental OR/MS models and methods. Each chapter gives an overview of a particular OR/MS model, its solution methods and illustrates successful applications. Part II of the handbook contains 11 chapters discussing the OR/MS applications in specific areas. They include airlines, e-commerce, energy systems, finance, military, production systems, project management, quality control, reliability, supply chain management and water resources. Part II ends with a chapter on the future of OR/MS applications.
Categories: Technology & Engineering

Stochastic Modeling of Scientific Data Second Edition

Stochastic Modeling of Scientific Data  Second Edition

"Accessible to any scientist or student with a reasonable background in statistics, this updated book presents a unique blend of stochastic process theory, statistical inference, and scientific applications of stochastic modeling of ...

Author: Peter Guttorp

Publisher:

ISBN: 1439875669

Category: Electronic books

Page:

View: 742

"Accessible to any scientist or student with a reasonable background in statistics, this updated book presents a unique blend of stochastic process theory, statistical inference, and scientific applications of stochastic modeling of scientific data. With an emphasis on real data applications, this second edition covers the numerous developments in methodology and computation since the original publication. It provides a more balanced treatment of Bayesian approaches to statistical inference and includes more recent scientific example problems that involve the statistical analysis of stochastic models. "--Provided by publisher.
Categories: Electronic books

Introduction to Stochastic Processes

Introduction to Stochastic Processes

He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration.

Author: Gregory F. Lawler

Publisher: CRC Press

ISBN: 9781482286113

Category: Mathematics

Page: 248

View: 231

Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.
Categories: Mathematics

Stochastic Geometry

Stochastic Geometry

Bernoulli 21(2), 930–956 (2015) G. Lindgren, Stationary Stochastic Processes:
Theory and Applications. Chapman & Hall/CRC Texts in Statistical Science
Series (CRC Press, Boca Raton, 2013) R. Lopes, N. Betrouni, Fractal and
multifractal ...

Author: David Coupier

Publisher: Springer

ISBN: 9783030135478

Category: Mathematics

Page: 232

View: 697

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.
Categories: Mathematics

Applied Probability and Stochastic Processes

Applied Probability and Stochastic Processes

Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension.

Author: Frank Beichelt

Publisher: CRC Press

ISBN: 9781482257670

Category: Business & Economics

Page: 562

View: 324

Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work. New to the Second Edition Completely rewritten part on probability theory—now more than double in size New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections Additional examples, exercises, and figures Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.
Categories: Business & Economics

Elementary Applications of Probability Theory Second Edition

Elementary Applications of Probability Theory  Second Edition

This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering.

Author: Henry C. Tuckwell

Publisher: CRC Press

ISBN: 0412576201

Category: Mathematics

Page: 296

View: 682

This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
Categories: Mathematics

Time Series Analysis

Time Series Analysis

Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems.

Author: Henrik Madsen

Publisher: CRC Press

ISBN: 9781420059670

Category: Mathematics

Page: 400

View: 712

With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explores the connections among stochastic dynamic models. Emphasizing the time domain description, the author presents theorems to highlight the most important results, proofs to clarify some results, and problems to illustrate the use of the results for modeling real-life phenomena. The book first provides the formulas and methods needed to adapt a second-order approach for characterizing random variables as well as introduces regression methods and models, including the general linear model. It subsequently covers linear dynamic deterministic systems, stochastic processes, time domain methods where the autocorrelation function is key to identification, spectral analysis, transfer-function models, and the multivariate linear process. The text also describes state space models and recursive and adaptivemethods. The final chapter examines a host of practical problems, including the predictions of wind power production and the consumption of medicine, a scheduling system for oil delivery, and the adaptive modeling of interest rates. Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems. It will help you understand the relationship between linear dynamic systems and linear stochastic processes.
Categories: Mathematics

Semimartingales and their Statistical Inference

Semimartingales and their Statistical Inference

Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for ...

Author: B.L.S. Prakasa Rao

Publisher: CRC Press

ISBN: 1584880082

Category: Mathematics

Page: 450

View: 551

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.
Categories: Mathematics

Introduction to Probability with R

Introduction to Probability with R

Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to ...

Author: Kenneth Baclawski

Publisher: CRC Press

ISBN: 142006522X

Category: Mathematics

Page: 384

View: 703

Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.
Categories: Mathematics

Modeling and Analysis of Stochastic Systems Second Edition

Modeling and Analysis of Stochastic Systems  Second Edition

Along with reorganizing the material, this edition revises and adds new exercises and examples.

Author: Vidyadhar G. Kulkarni

Publisher: Chapman and Hall/CRC

ISBN: 1439808759

Category: Business & Economics

Page: 544

View: 312

Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edition: a new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to finance; a more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processes; and, two appendices that collect relevant results from analysis and differential and difference equations. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations. A collection of MATLAB[registered]-based programs can be downloaded from the author's website and a solutions manual is available for qualifying instructors.
Categories: Business & Economics

The Analysis of Time Series

The Analysis of Time Series

Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, ...

Author: Chris Chatfield

Publisher: CRC Press

ISBN: 0203491688

Category: Mathematics

Page: 352

View: 776

Since 1975, The Analysis of Time Series: An Introduction has introduced legions of statistics students and researchers to the theory and practice of time series analysis. With each successive edition, bestselling author Chris Chatfield has honed and refined his presentation, updated the material to reflect advances in the field, and presented interesting new data sets. The sixth edition is no exception. It provides an accessible, comprehensive introduction to the theory and practice of time series analysis. The treatment covers a wide range of topics, including ARIMA probability models, forecasting methods, spectral analysis, linear systems, state-space models, and the Kalman filter. It also addresses nonlinear, multivariate, and long-memory models. The author has carefully updated each chapter, added new discussions, incorporated new datasets, and made those datasets available for download from www.crcpress.com. A free online appendix on time series analysis using R can be accessed at http://people.bath.ac.uk/mascc/TSA.usingR.doc. Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, analyzing time series in finance, and discrete-valued time series A new chapter of examples and practical advice Thorough updates and revisions throughout the text that reflect recent developments and dramatic changes in computing practices over the last few years The analysis of time series can be a difficult topic, but as this book has demonstrated for two-and-a-half decades, it does not have to be daunting. The accessibility, polished presentation, and broad coverage of The Analysis of Time Series make it simply the best introduction to the subject available.
Categories: Mathematics

Statistical Methods for Spatial Data Analysis

Statistical Methods for Spatial Data Analysis

This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain.

Author: Oliver Schabenberger

Publisher: CRC Press

ISBN: 9781482258134

Category: Mathematics

Page: 512

View: 692

Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.
Categories: Mathematics