Håvard Rue

This book provides a comprehensive and practical guide to fitting complex Bayesian survival, longitudinal and joint models using the Integrated Nested Laplace Approximations (INLA) methodology, a powerful and computationally efficient alternative to traditional MCMC methods. Aimed at graduate students, researchers, and applied statisticians in biostatistics, epidemiology, and public health, this book addresses the critical challenge of analyzing high-dimensional and correlated data. It demonstrates how to move beyond the computational limitations of conventional methods, enabling the analysis of sophisticated models that were previously out of reach. Through a series of clear, fully reproducible examples, readers will learn to: - Implement a wide range of survival models, including proportional hazards, competing risks, multi-state, cure, and frailty models. - Fit various longitudinal models for continuous, count, binary, semicontinuous, and ordinal data. - Construct and interpret joint models that link multiple longitudinal markers to single or multiple survival outcomes using various association structures. - Incorporate spatial random effects to account for spatial autocorrelation in areal and point-referenced data. This book is the result of a unique collaboration between the creators and key developers of the INLA methodology. The lead author, Denis Rustand, is the developer of the INLAjoint R package which serves as the primary software for the methods described. Håvard Rue is the principal architect of the INLA methodology and the R-INLA package. Janet van Niekerk is an expert in efficient Bayesian methods for complex survival analysis and a core INLA developer. Elias Teixeira Krainski is a renowned specialist in the theory and application of spatial statistics with INLA.

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.

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 modelsAll 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.

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 modelsAll 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.

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.