INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference.

Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download.

The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.

Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.

Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.

Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.

This book addresses the applications of extensively used regression models under a Bayesian framework. It emphasizes efficient Bayesian inference through integrated nested Laplace approximations (INLA) and real data analysis using R. The INLA method directly computes very accurate approximations to the posterior marginal distributions and is a promising alternative to Markov chain Monte Carlo (MCMC) algorithms, which come with a range of issues that impede practical use of Bayesian models.

"The book focuses on regression models with R-INLA and it will be of interest to a wide audience. INLA is becoming a very popular method for approximate Bayesian inference and it is being applied to many problems in many different fields. This book will be of interest not only to statisticians but also to applied researchers in other disciplines interested in Bayesian inference. This book can probably be used as a reference book for research and as a textbook at graduate level."~Virgilio Gómez-Rubio, University of Castilla-La Mancha "This is a well-written book on an important subject, for which there is a lack of good introductory material. The tutorial-style works nicely, and they have an excellent set of examples. They manage to do a practical introduction with just the right amount of theory background?The book should be very useful to scientists who want to analyze data using regression models. INLA allows users to fit Bayesian models quickly and without too much programming effort, and it has been used successfully in many applications. The book is written in a tutorial style, while explaining the basics of the needed theory very well, so it could serve both as a reference or textbook?The book is well written and technically correct." ~Egil Ferkingstad, deCode genetics "The authors have done a great job of not over-doing the technical details, thereby making the presentation accessible to a broader audience beyond the statistics world?It covers many contemporary parametric, nonparametric, and semiparametric methods that applied scientists from many fields use in modern research."~Adam Branscum, Oregon State University