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Spatial point patterns: methodology and applications with R

By: Baddeley, Adrian.
Contributor(s): Rubak, Ege | Turner, Rolf.
Material type: materialTypeLabelBookSeries: Chapman and Hall/CRC interdisciplinary statistics series. Publisher: Boca Raton CRC Press 2016Description: xiii, 810 p.ISBN: 9781482210200.Subject(s): Spatial data infrastructures - Mathematics | R (Computer program language)DDC classification: 519.5 Summary: Spatial Point Patterns: Methodology and Applications with R shows scientific researchers and applied statisticians from a wide range of fields how to analyze their spatial point pattern data. Making the techniques accessible to non-mathematicians, the authors draw on their 25 years of software development experiences, methodological research, and broad scientific collaborations to deliver a book that clearly and succinctly explains concepts and addresses real scientific questions. Practical Advice on Data Analysis and Guidance on the Validity and Applicability of Methods The first part of the book gives an introduction to R software, advice about collecting data, information about handling and manipulating data, and an accessible introduction to the basic concepts of point processes. The second part presents tools for exploratory data analysis, including non-parametric estimation of intensity, correlation, and spacing properties. The third part discusses model-fitting and statistical inference for point patterns. The final part describes point patterns with additional "structure," such as complicated marks, space-time observations, three- and higher-dimensional spaces, replicated observations, and point patterns constrained to a network of lines. Easily Analyze Your Own Data Throughout the book, the authors use their spatstat package, which is free, open-source code written in the R language. This package provides a wide range of capabilities for spatial point pattern data, from basic data handling to advanced analytic tools. The book focuses on practical needs from the user’s perspective, offering answers to the most frequently asked questions in each chapter. (https://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/9781482210200)
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Table of Contents:

I BASICS

1. Introduction

• Point patterns
• Statistical methodology for point patterns
• About this book

2. Software Essentials

• Introduction to RR
• Packages for R
• Introduction to spatstat
• Getting started with spatstat
• FAQ

3. 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

4. Inspecting and Exploring Data

• Plotting
• Manipulating point patterns and windows
• Exploring images
• Using line segment patterns
• Tessellations
• FAQ

5. Point Process Methods

• Motivation
• Basic definitions
• Complete spatial randomness
• Inhomogeneous Poisson process
• A menagerie of models
• Fundamental issues
• Goals of analysis


II EXPLORATORY DATA ANALYSIS

6. Intensity

Introduction
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

7. Correlation

• Introduction
• 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
• Theory
• FAQ

8. Spacing

• Introduction
• Basic methods
• Nearest-neighbour function G and empty-space function F
• Confidence intervals and simulation envelopes
• Empty-space hazard
• J-function
• 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
• FAQ


III STATISTICAL INFERENCE


9. Poisson Models

• Introduction
• Poisson point process models
• Fitting Poisson models in spatstat
• Statistical inference for Poisson models
• Alternative fitting methods
• More flexible models
• Theory
• Coarse quadrature approximation
• Fine pixel approximation
• Conditional logistic regression
• Approximate Bayesian inference
• Non-loglinear models
• Local likelihood
• FAQ

10. Hypothesis Tests and Simulation Envelopes

• Introduction
• 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

11. 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

12. Cluster and Cox Models

• Introduction
• Cox processes
• Cluster processes
• Fitting Cox and cluster models to data
• Locally fitted models
• Theory
• FAQ

13. Gibbs Models

• Introduction
• Conditional intensity
• Key concepts
• Statistical insights
• Fitting Gibbs models to data
• Pairwise interaction models
• Higher-order interactions
• Hybrids of Gibbs models
• Simulation
• Goodness-of-fit and validation for fitted Gibbs models
• Locally fitted models
• Theory: Gibbs processes
• Theory: Fitting Gibbs models
• Determinantal point processes
• FAQ

14. Patterns of Several Types of Points

• Introduction
• 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
• Theory
• FAQ


IV ADDITIONAL STRUCTURE


15. Higher-Dimensional Spaces and Marks

• Introduction
• Point patterns with numerical or multidimensional marks
• Three-dimensional point patterns
• Point patterns with any kinds of marks and coordinates
• FAQ

16. Replicated Point Patterns and Designed Experiments

• Introduction
• Methodology
• Lists of objects
• Hyperframes
• Computing with hyperframes
• Replicated point pattern datasets in spatstat
• Exploratory data analysis
• Analysing summary functions from replicated patterns
• Poisson models
• Gibbs models
• Model validation
• Theory
• FAQ

17. Point Patterns on a Linear Network

• Introduction
• Network geometry
• Data handling
• Intensity
• Poisson models
• Intensity on a tree
• Pair correlation function
• K-function
• FAQ


Spatial Point Patterns: Methodology and Applications with R shows scientific researchers and applied statisticians from a wide range of fields how to analyze their spatial point pattern data. Making the techniques accessible to non-mathematicians, the authors draw on their 25 years of software development experiences, methodological research, and broad scientific collaborations to deliver a book that clearly and succinctly explains concepts and addresses real scientific questions.

Practical Advice on Data Analysis and Guidance on the Validity and Applicability of Methods

The first part of the book gives an introduction to R software, advice about collecting data, information about handling and manipulating data, and an accessible introduction to the basic concepts of point processes. The second part presents tools for exploratory data analysis, including non-parametric estimation of intensity, correlation, and spacing properties. The third part discusses model-fitting and statistical inference for point patterns. The final part describes point patterns with additional "structure," such as complicated marks, space-time observations, three- and higher-dimensional spaces, replicated observations, and point patterns constrained to a network of lines.

Easily Analyze Your Own Data

Throughout the book, the authors use their spatstat package, which is free, open-source code written in the R language. This package provides a wide range of capabilities for spatial point pattern data, from basic data handling to advanced analytic tools. The book focuses on practical needs from the user’s perspective, offering answers to the most frequently asked questions in each chapter.


(https://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/9781482210200)

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