# Welcome

This is the companion website for **“Spatial Point Patterns: Methodology and Applications with R“**.

Here you can download three sample chapters for free and find R code to reproduce all figures and output in the book.

## Table of contents

PART I: **BASICS**

1. **Introduction**

Point patterns

Statistical methodology for point patterns

About this book

2. **Software Essentials**

Introduction to R

Packages for R

Introduction to spatstat

Getting started with spatstat

FAQ

3. **Collecting and Handling Point Pattern Data** (download pdf)

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

PART 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** (download pdf)

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

PART III: **STATISTICAL INFERENCE**

9. **Poisson Models** (download pdf)

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

PART 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