Baddeley / Rubak / Turner Spatial Point Patterns

Methodology and Applications with R
1. Auflage 2015
ISBN: 978-1-4822-1021-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 828 Seiten

Reihe: Chapman & Hall/CRC Interdisciplinary Statistics

Modern Statistical Methodology and Software for Analyzing Spatial Point Patterns

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.

Zielgruppe

Researchers and Graduate Students from Statistics. Researchers from Ecology, Epidemiology, Environmental Science, Astronomy, and Econometrics.

Autoren/Hrsg.

Baddeley, Adrian

Rubak, Ege

Turner, Rolf

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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

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

EXPLORATORY DATA ANALYSIS
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

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

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

STATISTICAL INFERENCE
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

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

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

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

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

ADDITIONAL STRUCTURE
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

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

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

Über Autor(innen)

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.