Statistical Inference For Spatial Processes

Author : B. D. Ripley
Publisher : Cambridge University Press
Page : 162 pages
File Size : 54,6 Mb
Release : 1988
Category : Mathematics
ISBN : 0521424208

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Statistical Inference for Spatial Processes by B. D. Ripley Pdf

The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal to researchers in computer vision, image processing, and those applying microscopy in biology, geology and materials science, as well as to statisticians interested in the foundations of their discipline.

Author : Jesper Moller,Rasmus Plenge Waagepetersen
Publisher : CRC Press
Page : 320 pages
File Size : 54,6 Mb
Release : 2003-09-25
Category : Mathematics
ISBN : 0203496930

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Statistical Inference and Simulation for Spatial Point Processes by Jesper Moller,Rasmus Plenge Waagepetersen Pdf

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Author : Chrysoula Dimitriou-Fakalou
Publisher : Unknown
Page : 532 pages
File Size : 45,7 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:940070551

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Statistical inference for spatial and spatio-temporal processes by Chrysoula Dimitriou-Fakalou Pdf

Author : Yu A. Kutoyants
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217060

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Statistical Inference for Spatial Poisson Processes by Yu A. Kutoyants Pdf

This work is devoted to several problems of parametric (mainly) and nonparametric estimation through the observation of Poisson processes defined on general spaces. Poisson processes are quite popular in applied research and therefore they attract the attention of many statisticians. There are a lot of good books on point processes and many of them contain chapters devoted to statistical inference for general and partic ular models of processes. There are even chapters on statistical estimation problems for inhomogeneous Poisson processes in asymptotic statements. Nevertheless it seems that the asymptotic theory of estimation for nonlinear models of Poisson processes needs some development. Here nonlinear means the models of inhomogeneous Pois son processes with intensity function nonlinearly depending on unknown parameters. In such situations the estimators usually cannot be written in exact form and are given as solutions of some equations. However the models can be quite fruitful in en gineering problems and the existing computing algorithms are sufficiently powerful to calculate these estimators. Therefore the properties of estimators can be interesting too.

Author : Yu A Kutoyants
Publisher : Unknown
Page : 292 pages
File Size : 55,7 Mb
Release : 1998-09-11
Category : Electronic
ISBN : 1461217075

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Statistical Inference for Spatial Poisson Processes by Yu A Kutoyants Pdf

Author : Marc Moore
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301479

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Spatial Statistics: Methodological Aspects and Applications by Marc Moore Pdf

This volume contains presentations by eminent researchers: Statistical Inference for Spatial Processes; Image Analysis; Applications of Spatial Statistics in Earth, Environmental, and Health Sciences; and Statistics of Brain Mapping. They range from asymptotic considerations for spatial processes to practical considerations related to particular applications including important methodological aspects. Many contributions concern image analysis, mainly images related to brain mapping.

Author : Alan Karr
Publisher : Routledge
Page : 509 pages
File Size : 42,9 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351423830

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Point Processes and Their Statistical Inference by Alan Karr Pdf

Maintaining the excellent features that made the first edition so popular, this outstanding reference/text presents the only comprehensive treatment of the theory of point processes and statistical inference for point processes-highlighting both pointprocesses on the real line and sp;,.tial point processes. Thoroughly updated and revised to reflect changes since publication of the firstedition, the expanded Second EdiLion now contains a better organized and easierto-understand treatment of stationary point processes ... expanded treatment ofthe multiplicative intensity model ... expanded treatment of survival analysis . ..broadened consideration of applications ... an expanded and extended bibliographywith over 1,000 references ... and more than 3('() end-of-chapter exercises.

Author : M.N.M. van Lieshout
Publisher : CRC Press
Page : 162 pages
File Size : 45,8 Mb
Release : 2019-03-19
Category : Mathematics
ISBN : 9780429627033

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Theory of Spatial Statistics by M.N.M. van Lieshout Pdf

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Author : Alan E. Gelfand,Peter Diggle,Peter Guttorp,Montserrat Fuentes
Publisher : CRC Press
Page : 622 pages
File Size : 50,5 Mb
Release : 2010-03-19
Category : Mathematics
ISBN : 9781420072884

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Handbook of Spatial Statistics by Alan E. Gelfand,Peter Diggle,Peter Guttorp,Montserrat Fuentes Pdf

Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters.The handbook begins with a historical intro

Author : Noel Cressie
Publisher : John Wiley & Sons
Page : 931 pages
File Size : 51,8 Mb
Release : 2015-03-18
Category : Mathematics
ISBN : 9781119115182

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Statistics for Spatial Data by Noel Cressie Pdf

The Wiley Classics Library consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. Spatial statistics — analyzing spatial data through statistical models — has proven exceptionally versatile, encompassing problems ranging from the microscopic to the astronomic. However, for the scientist and engineer faced only with scattered and uneven treatments of the subject in the scientific literature, learning how to make practical use of spatial statistics in day-to-day analytical work is very difficult. Designed exclusively for scientists eager to tap into the enormous potential of this analytical tool and upgrade their range of technical skills, Statistics for Spatial Data is a comprehensive, single-source guide to both the theory and applied aspects of spatial statistical methods. The hard-cover edition was hailed by Mathematical Reviews as an "excellent book which will become a basic reference." This paper-back edition of the 1993 edition, is designed to meet the many technological challenges facing the scientist and engineer. Concentrating on the three areas of geostatistical data, lattice data, and point patterns, the book sheds light on the link between data and model, revealing how design, inference, and diagnostics are an outgrowth of that link. It then explores new methods to reveal just how spatial statistical models can be used to solve important problems in a host of areas in science and engineering. Discussion includes: Exploratory spatial data analysis Spectral theory for stationary processes Spatial scale Simulation methods for spatial processes Spatial bootstrapping Statistical image analysis and remote sensing Computational aspects of model fitting Application of models to disease mapping Designed to accommodate the practical needs of the professional, it features a unified and common notation for its subject as well as many detailed examples woven into the text, numerous illustrations (including graphs that illuminate the theory discussed) and over 1,000 references. Fully balancing theory with applications, Statistics for Spatial Data, Revised Edition is an exceptionally clear guide on making optimal use of one of the ascendant analytical tools of the decade, one that has begun to capture the imagination of professionals in biology, earth science, civil, electrical, and agricultural engineering, geography, epidemiology, and ecology.

Author : Oliver Schabenberger,Carol A. Gotway
Publisher : CRC Press
Page : 444 pages
File Size : 51,8 Mb
Release : 2017-01-27
Category : Mathematics
ISBN : 9781351991476

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Statistical Methods for Spatial Data Analysis by Oliver Schabenberger,Carol A. Gotway Pdf

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.

Author : M.N.M. van Lieshout
Publisher : CRC Press
Page : 168 pages
File Size : 42,5 Mb
Release : 2019-03-19
Category : Mathematics
ISBN : 9780429628672

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Theory of Spatial Statistics by M.N.M. van Lieshout Pdf

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Author : N.U. Prabhu
Publisher : CRC Press
Page : 294 pages
File Size : 40,8 Mb
Release : 2020-08-13
Category : Mathematics
ISBN : 9781000147742

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Statistical Inference in Stochastic Processes by N.U. Prabhu Pdf

Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di

Author : Ronny Vallejos,Felipe Osorio,Moreno Bevilacqua
Publisher : Springer Nature
Page : 194 pages
File Size : 51,6 Mb
Release : 2020-09-22
Category : Mathematics
ISBN : 9783030566814

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Spatial Relationships Between Two Georeferenced Variables by Ronny Vallejos,Felipe Osorio,Moreno Bevilacqua Pdf

This book offers essential, systematic information on the assessment of the spatial association between two processes from a statistical standpoint. Divided into eight chapters, the book begins with preliminary concepts, mainly concerning spatial statistics. The following seven chapters focus on the methodologies needed to assess the correlation between two or more processes; from theory introduced 35 years ago, to techniques that have only recently been published. Furthermore, each chapter contains a section on R computations to explore how the methodology works with real data. References and a list of exercises are included at the end of each chapter. The assessment of the correlation between two spatial processes has been tackled from several different perspectives in a variety of applications fields. In particular, the problem of testing for the existence of spatial association between two georeferenced variables is relevant for posterior modeling and inference. One evident application in this context is the quantification of the spatial correlation between two images (processes defined on a rectangular grid in a two-dimensional space). From a statistical perspective, this problem can be handled via hypothesis testing, or by using extensions of the correlation coefficient. In an image-processing framework, these extensions can also be used to define similarity indices between images.

Author : Lyle D. Broemeling
Publisher : CRC Press
Page : 373 pages
File Size : 53,8 Mb
Release : 2017-12-12
Category : Mathematics
ISBN : 9781315303574

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Bayesian Inference for Stochastic Processes by Lyle D. Broemeling Pdf

This is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter devoted to the fundamental concepts in stochastic processes is included. Bayesian inference (estimation, testing hypotheses, and prediction) for discrete time Markov chains, for Markov jump processes, for normal processes (e.g. Brownian motion and the Ornstein–Uhlenbeck process), for traditional time series, and, lastly, for point and spatial processes are described in detail. Heavy emphasis is placed on many examples taken from biology and other scientific disciplines. In order analyses of stochastic processes, it will use R and WinBUGS. Features: Uses the Bayesian approach to make statistical Inferences about stochastic processes The R package is used to simulate realizations from different types of processes Based on realizations from stochastic processes, the WinBUGS package will provide the Bayesian analysis (estimation, testing hypotheses, and prediction) for the unknown parameters of stochastic processes To illustrate the Bayesian inference, many examples taken from biology, economics, and astronomy will reinforce the basic concepts of the subject A practical approach is implemented by considering realistic examples of interest to the scientific community WinBUGS and R code are provided in the text, allowing the reader to easily verify the results of the inferential procedures found in the many examples of the book Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.