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Spatial Point Patterns


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Table of Contents

Point patterns
Statistical methodology for point patterns
About this book

Software Essentials
Introduction to RR
Packages for R
Introduction to spatstat
Getting started with spatstat
FAQ Collecting and Handling Point Pattern Data
Surveys and experiments
Data handling
Entering point pattern data into spatstat
Data errors and quirks
Windows in spatstat
Pixel images in spatstat
Line segment patterns
Collections of objects
Interactive data entry in spatstat
Reading GIS file formats
FAQ Inspecting and Exploring Data
Manipulating point patterns and windows
Exploring images
Using line segment patterns
FAQ Point Process Methods
Basic definitions
Complete spatial randomness
Inhomogeneous Poisson process
A menagerie of models
Fundamental issues
Estimating homogeneous intensity
Technical definition
Quadrat counting
Smoothing estimation of intensity function
Investigating dependence of intensity on a covariate
Formal tests of (non-)dependence on a covariate
Hot spots, clusters, and local features
Kernel smoothing of marks
FAQ Correlation
Manual methods
The K-function
Edge corrections for the K-function
Function objects in spatstat
The pair correlation function
Standard errors and confidence intervals
Testing whether a pattern is completely random
Detecting anisotropy
Adjusting for inhomogeneity
Local indicators of spatial association
Third- and higher-order summary statistics
FAQ Spacing
Basic methods
Nearest-neighbour function G and empty-space function F
Confidence intervals and simulation envelopes
Empty-space hazard
Inhomogeneous F-, G- and J-functions
Anisotropy and the nearest-neighbour orientation
Empty-space distance for a spatial pattern
Distance from a point pattern to another spatial pattern
Theory for edge corrections
Palm distribution
Poisson Models
Poisson point process models
Fitting Poisson models in spatstat
Statistical inference for Poisson models
Alternative fitting methods
More flexible models
Coarse quadrature approximation
Fine pixel approximation
Conditional logistic regression
Approximate Bayesian inference
Non-loglinear models
Local likelihood
FAQ Hypothesis Tests and Simulation Envelopes
Concepts and terminology
Testing for a covariate effect in a parametric model
Quadrat counting tests
Tests based on the cumulative distribution function
Monte Carlo tests
Monte Carlo tests based on summary functions
Envelopes in spatstat
Other presentations of envelope tests
Dao-Genton test and envelopes
Power of tests based on summary functions
FAQ Model Validation
Overview of validation techniques
Relative intensity
Residuals for Poisson processes
Partial residual plots
Added variable plots
Validating the independence assumption
Leverage and influence
Theory for leverage and influence
FAQ Cluster and Cox Models
Cox processes
Cluster processes
Fitting Cox and cluster models to data
Locally fitted models
FAQ Gibbs Models
Conditional intensity
Key concepts
Statistical insights
Fitting Gibbs models to data
Pairwise interaction models
Higher-order interactions
Hybrids of Gibbs models
Goodness-of-fit and validation for fitted Gibbs models
Locally fitted models
Theory: Gibbs processes
Theory: Fitting Gibbs models
Determinantal point processes
FAQ Patterns of Several Types of Points
Methodological issues
Handling multitype point pattern data
Exploratory analysis of intensity
Multitype Poisson models
Correlation and spacing
Tests of randomness and independence
Multitype Gibbs models
Hierarchical interactions
Multitype Cox and cluster processes
Other multitype processes
Higher-Dimensional Spaces and Marks
Point patterns with numerical or multidimensional marks
Three-dimensional point patterns
Point patterns with any kinds of marks and coordinates
FAQ Replicated Point Patterns and Designed Experiments
Lists of objects
Computing with hyperframes
Replicated point pattern datasets in spatstat
Exploratory data analysis
Analysing summary functions from replicated patterns
Poisson models
Gibbs models
Model validation
FAQ Point Patterns on a Linear Network
Network geometry
Data handling
Poisson models
Intensity on a tree
Pair correlation function

About the Author

Adrian Baddeley is a professor of computational statistics at Curtin University and a fellow of the Australian Academy of Science. He has been a leading researcher in spatial statistics for 40 years. Ege Rubak is an associate professor in the world-renowned spatial statistics group at Aalborg University. His research focuses on spatial statistics and statistical computing. Rolf Turner is retired and an Honorary Research Fellow at the University of Auckland, where he has taught a graduate course on spatial point processes in the Department of Statistics. He has considerable expertise in statistical computing and has worked as a statistician in the Division of Mathematics and Statistics at CSIRO, the University of New Brunswick, and the Starpath Project at the University of Auckland.


"... A very broad range of topics is covered over 810 pages, using examples from different fields of science, most notably astronomy, biology, ecology, geology, and environmental sciences. In reading the book, one of the most enjoyable features is the critical attitude encouraged by the authors, who always question the suitability of specific statistical methods in relation to a given scientific question. The reader is guided from the first to the last step of a statistical analysis of SPP data with useful advice on modeling strategies and illustration of open-source statistical software. The style is highly accessible to a nonstatistical audience, with mathematical formalism kept to a minimum. ... What sets this book apart from others in its field are the strong link that the authors build between statistical methodology and scientific problems drawn from multidisciplinary case studies, the coverage of a wide range of topics, and its reference to highquality open-source statistical software. For these reasons, the book is likely to become a classic in SPP data analysis."
-Emanuele Giorgi, Lancester University, in The American Statistician, July 2017

"The entire publication offers a wealth of information and will serve as an excellent manual and guide for the work of the point process statistician. One of the many strengths of the book is that it consistently considers point process statistics as a part of statistics in general and always to refer to general statistical ideas. The text is very accessible...There are a lot of interesting examples, which can be reproduced by the reader in R. The reader will appreciate the frequent discussions of caveats and the well-selected and well-answered FAQ's (frequently asked questions) at the end of each chapter...Overall, this publication presents an excellent introduction to and manual for the spatstat package, for which the community of spatial statisticians will be very grateful to the authors. For readers who use this software, it is an indispensable manual that the reviewer strongly recommends...The reviewer is sure that it will initiate a big step forward in the use of statistical methods for point patterns."
-Dietrich Stoyan, TU Bergakademie Freiberg, Biometrical Journal, January 2017

"In a nutshell, this book covers a large portion of the methods for the analysis of spatial point patterns and their implementation in the spatstat package... As spatstat has evolved with help from its users and the community, a list of frequently asked questions (FAQ) is included at the end of most chapters. This will help to clarify some of the contents and guide the user in the data analysis by pointing at different important points to consider. The book is also full of tips, clarifications and discussions on how to conduct the analysis, which clearly will benefit practitioners. It presents and discusses many applications from different fields, so that it will be of interest to a wide range of researchers...I really enjoyed reading this book and it has changed my views on spatstat. In addition to a package for the analysis of point patterns, I now regard this package as a toolbox that will allow the development of further methods and software for the analysis of point patterns, as the package provides a number of functions to rely on when developing new methods."
-Virgilio Gomez-Rubio, Universidad de Castilla-La Mancha, Journal of Statistical Software, December 2016

"Several books on analysing point pattern processes have been published in recent years; this is by far the largest, at least in part due to the inclusion of example scripts and output. Its central tool is the spatstat package in R. Chapters cover spatial point pattern statistics from first principles through to some of the more sophisticated techniques. Its audience is scientists looking to employ and interpret these tools, and while technical sections are included, they expand on the applied material rather than being core. This will prove a valuable reference and its guidance will improve standards in the field."
-Markus Eichhorn, Frontiers of Biogeography, 2016, Volume 8, Issue 3

"As the authors point out in their preface, the book is not intended to be an introduction to point process theory for mathematicians. Rather, they aim to focus on the principles of statistical inference for spatial data and to help researchers in application domains with the practicalities of the analysis and the interpretation of the results. In this, they have succeeded brilliantly...The book is written in a distinct, at times funny, always accessible style. General principles of every aspect of spatial point pattern analysis, from data collection to model validation, are discussed in great detail with pointers to the specialized literature for those who wish to gain a deeper understanding of the technicalities. The principles are illustrated by means of a wide collection of examples that can be reproduced by the reader in R. Moreover, a selection of frequently asked questions from spatstat users is answered at the end of each chapter...In summary, I warmly recommend the book to anyone who wishes to analyze point patterns professionally."
-Marie-Colette van Lieshout, reviewed in Biometrics, June 2016

"Baddeley, Rubak, and Turner have written a uniquely comprehensive account of modern statistical methods for the analysis of spatial point pattern data, aimed firmly at users and, crucially, made accessible to users by explicit linkage of the methods to their own excellent R package, spatstat. Essential reading for anyone who needs to analyze spatial point pattern data properly or to teach others how to do so."
-Peter J. Diggle, Distinguished University Professor, CHICAS, Lancaster University Medical School, UK

"Baddeley, Rubak, and Turner's book on spatial point patterns is part of a revolution in statistics, and the reader is buoyantly swept along with it. From data handling, to exploratory data analysis, to advanced analytic tools, we are treated to the best in data science, where open-source software in the R language is used to integrate science and data through statistical thinking. This is an excellent book, founded on methodology derived from statistical models of spatial point patterns, but focusing on the practical needs of the applied scientist."
-Noel Cressie, Distinguished Professor, National Institute for Applied Statistics Research Australia, University of Wollongong

"Spatial Point Patterns: Methodology and Applications with R is a rich statistical feast. It is by turns humorous, serious, occasionally rather direct, but never talks down to the reader, who is taken as having a well-motivated interest in spatial point patterns. I would argue that applied statisticians not yet conscious of such an interest will also relish the book's stated intention of bringing its topical treatments back into mainstream statistical practice. Being able to try everything out in R, largely using the spatstat package is a clear advantage; this is coupled with numerous relevant example data sets. While cherry picking is possible-the index is more than adequate-all readers are advised to read at least whole chapters, best complete parts of the book, because the information to be found there is part of a tightly woven fabric. Much can be re-read several times with both profit and pleasure by statisticians and non-statistician practitioners. Sustaining this level of attention to detail through a long book is a splendid achievement."
-Roger Bivand, Professor of Geography, Norwegian School of Economics, and Author and Maintainer of Packages for Spatial Data Analysis, R Project

"The analysis of spatial point patterns and processes is an exploding field of applied research across many science and social science disciplines. This is thanks in no small part to the development of open-licensed, well-documented, methodologically sophisticated software implementations. For at least a decade, the authors of this book have been at the forefront of a statistical programming revolution. However, with wider academic access to these point pattern-and-process methods, there has also come a pressing need for clearer guidance on good practice for applied researchers at all stages from graduate studies onward. Expressed in an elegant and accessible style, with substantial references for those wanting directions into the more specialist literature, as well as an excellent set of reproducible, multi-disciplinary case studies, this book provides exactly what is needed. It is highly likely to become a classic."
-Andrew Bevan, Institute of Archaeology, University College London

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