Spatial Point Patterns Methodology and Applications with R

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.

BASICS Introduction Point patterns Statistical methodology for point patterns About this book Software Essentials Introduction to RR Packages for RIntroduction to spatstatGetting started with spatstatFAQ Collecting and Handling Point Pattern Data Surveys and experiments Data handling Entering point pattern data into spatstatData errors and quirks Windows in spatstatPixel images in spatstatLine segment patterns Collections of objects Interactive data entry in spatstat Reading GIS file formats FAQ Inspecting and Exploring DataPlotting Manipulating point patterns and windows Exploring images Using line segment patterns Tessellations FAQ Point Process Methods Motivation Basic definitionsComplete spatial randomness Inhomogeneous Poisson process A menagerie of models Fundamental issues Goals of analysis EXPLORATORY DATA ANALYSIS Intensity Introduction Estimating homogeneous intensity Technical definitionQuadrat 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-functionFunction 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 TheoryFAQ 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 correctionsPalm distributionFAQ 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 TheoryCoarse quadrature approximationFine pixel approximationConditional logistic regressionApproximate 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 influenceFAQ Cluster and Cox ModelsIntroduction Cox processes Cluster processes Fitting Cox and cluster models to data Locally fitted models TheoryFAQ 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 processesTheory: Fitting Gibbs modelsDeterminantal 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 TheoryFAQ 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 TheoryFAQ Point Patterns on a Linear Network Introduction Network geometry Data handling Intensity Poisson models Intensity on a tree Pair correlation function K-function FAQ

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.