Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Elias T. Krainski, Virgilio Gómez-Rubio, Haakon Bakka, Amanda Lenzi, Daniela Castro-Camilo, Daniel Simpson, Finn Lindgren, Håvard Rue, Elias Krainski

• Publisher: Chapman and Hall/CRC
• Year: 2018
• Print ISBN: 9781138369856
• eBook ISBN: 9780429628214
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications.

This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications:

* Spatial and spatio-temporal models for continuous outcomes

* Analysis of spatial and spatio-temporal point patterns

* Coregionalization spatial and spatio-temporal models

* Measurement error spatial models

* Modeling preferential sampling

* Spatial and spatio-temporal models with physical barriers

* Survival analysis with spatial effects

* Dynamic space-time regression

* Spatial and spatio-temporal models for extremes

* Hurdle models with spatial effects

* Penalized Complexity priors for spatial models

All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book.

The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• What this book is and isn’t
• 1 The Integrated Nested Laplace Approximation and the R-INLA package
• 2 Introduction to spatial modeling
• 3 More than one likelihood
• 4 Point processes and preferential sampling
• 5 Spatial non-stationarity
• 6 Risk assessment using non-standard likelihoods
• 7 Space-time models
• 8 Space-time applications
• A List of symbols and notation
• B Packages used in the book
• Bibliography
• Index