Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA: 1st Edition (e-Book) book cover

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

1st Edition

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

Chapman and Hall/CRC

284 pages

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Hardback: 9781138369856
pub: 2018-12-19
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pub: 2018-12-07
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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

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


What this book is and isn’t

  1. The Integrated Nested Laplace Approximation and the R-INLA package
  2. Introduction

    The INLA method

    A simple example

    Additional arguments and control options

    Manipulating the posterior marginals

    Advanced features

  3. Introduction to spatial modeling
  4. Introduction

    The SPDE approach

    A toy example

    Projection of the random field


    Triangulation details and examples

    Tools for mesh assessment

    Non-Gaussian response: Precipitation in Paraná

  5. More than one likelihood
  6. Coregionalization model

    Joint modeling: Measurement error model

    Copying part of or the entire linear predictor

  7. Point processes and preferential sampling
  8. Introduction

    Including a covariate in the log-Gaussian Cox process

    Geostatistical inference under preferential sampling

  9. Spatial non-stationarity
  10. Explanatory variables in the covariance

    The Barrier model

    Barrier model for noise data in Albacete (Spain)

  11. Risk assessment using non-standard likelihoods
  12. Survival analysis

    Models for extremes

  13. Space-time models
  14. Discrete time domain

    Continuous time domain

    Lowering the resolution of a spatio-temporal model

    Conditional simulation: Combining two meshes

  15. Space-time applications

Space-time coregionalization model

Dynamic regression example

Space-time point process: Burkitt example

Large point process dataset

Accumulated rainfall: Hurdle Gamma model

List of symbols and notation

Packages used in the book

About the Authors

Elias T. Krainski is a Professor Adjunto in the Department of Statistics, Universidade Federal do Paraná (Curitiba, Brazil). He has been working on new space-time models and applications in epidemiology and fisheries with INLA and SPDE.

Virgilio Gómez-Rubio is an Associate Professor in the Department of Mathematics, Universidad de Castilla-La Mancha (Albacete, Spain). His research interests are on Bayesian inference, spatial statistics and computational statistics. He has also developed several packages for the R language on spatial data analysis and Bayesian computation.

Haakon Bakka is a Post Doctoral Fellow at the King Abdullah University of Science and Technology. He has given many courses in both INLA and the SPDE approach, and parts of his research on spatial models are included in this book.

Amanda Lenzi is a Post-Doctoral Fellow at the King Abdullah University of Science and Technology in Saudi Arabia, where she is part of the Spatio-Temporal Statistics and Data Science Group. Her research interest is on spatial and spatio-temporal statistics with applications in environmental science, especially in wind energy.

Daniela Castro-Camilo is a Post-Doctoral Fellow working in the Extreme Statistics Research Group at the King Abdullah University of Science and Technology, in Saudi Arabia. Her research interest is on the theory and applications of multivariate and spatial extremes, with a particular focus in environmental applications.

Daniel Simpson is an Assistant Professor in the Department of Statistical Sciences, University of Toronto. His research interests are on Computational Statistics, Spatial Statistics, Bayesian Statistics, and Numerical Linear Algebra. He has also been working on Penalized Complexity priors and the analysis of point patterns with INLA and SPDEs.

Finn Lindgren is a Chair of Statistics in the School of Mathematics at the University of Edinburgh, Scotland. His research covers spatial stochastic modeling and associated computational methods, including applications in climate science, ecology, medical statistics, geosciences, and general environmetrics. He developed the core methods and code for the SPDE interface of the R-INLA package, is a co-developer of the related packages "excursions" and "inlabru," and has given lecture series and practical workshops on spatial modeling with INLA.

Håvard Rue is a Professor of Statistics, at the CEMSE Division at the King Abdullah University of Science and Technology, Saudi Arabia, where he leads a research group on Bayesian Computational Statistics & Modeling. He is the main developer of the INLA methodology and the R-INLA Project.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General