Book

INLA stands for Integrated Nested Laplace Approximations. It is a method for fitting a broad class of Bayesian models. Historically, it was difficult to fit anything but the most simple Bayesian models. Over the last twenty years, a class of Bayesian computational methods based on a simulation method called Markov chain Monte Carlo (MCMC) has been developed and has seen wide acceptance in statistics. Popular packages using these methods include BUGS, JAGS and STAN. Despite impressive improvements, these packages suffer from two problems. First, they are slow. For some more complex and/or larger data problems, MCMC can be infeasibly slow, even if you are prepared to wait days. But even for more modest problems, the ability to fit models quickly is crucial to exploratory data analyses. INLA is an approximation method. Typically, the approximations are more than adequate and remember that simulation methods are inevitably approximations also if they are to finish in finite time. INLA takes no more than a few seconds to fit the models found in this book.

The other practical difficulty with MCMC methods is they take substantial expertise to use. You need to learn a specialized programming language to specify the models. You also need to understand the diagnostics that determine whether the model has been fit correctly or whether the simulation process has failed. Some skill is necessary to make a success of this. Despite ongoing improvement in this area, this has been an obstacle to wider adoption of these methods in the scientific community.

There are some drawbacks to INLA too. Although you do not need to learn a specific programming language as the models can be specified and analyzed using R, it is still not that straightforward. Indeed, that is why you should read this book. Furthermore, INLA only applies to a class called latent Gaussian models. If you browse through the table of contents for this book, you will see that this class is very broad. Nevertheless, there will be some models that cannot be fit with INLA but can be done with MCMC.

We make some assumptions about you, the reader. We expect that you have a basic knowledge of statistical theory and practice. We expect you already know something about Bayesian methodology. This is not a theoretical book as we focus our presentation around examples. We hope that scientists, who already use some statistics, will find this book accessible. We also expect you have some knowledge of R. We do provide fully working code for all the examples so you may be able to adapt this to your own needs without proficiency in R. Even so, you will need some experience with R to draw the full benefit. If you need more introductory material, we direct you to more comprehensive and accessible texts.

This book is about regression models and we have not presented the extensive spatial data analysis capabilities of INLA. For those specifically interested in spatial data, we direct you to Blangiardo and Cameletti (2015).

https://github.com/julianfaraway/brinla