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.