Bayesian Inference using INLA

This is a course for everyone who want to start learning Bayesian Inference using INLA. It has been constructed combining material of different sources: tutorial and books which are referenced at the end of each presentation.

Program

The course is divided in three parts combining theoretical and practical aspects, and normally is taught in two classes (4 hours per class)

class1-PART 1: An Introduction to Bayesian inference. Bayes theorem. Posterior distribution of the parameters. Prediction. Hierarchical Bayesian models.

class1-PART 2: Bayesian inference using the integrated nested Laplace approximation (INLA) Latent Gaussian models (LGMs). Laplace approximation. Gaussian Markov random fields (GMRFs). Fitting GLMMs using INLA. Structured temporal and spatial random effects.

class2-PART 3: Geostatistics using INLA and inlabru. Geostatistics in the context of LGMs. The Stochastic partial differential equation (SPDE).

Software

To take full advantage of the course, it is necessary that everyone has the following programs installed:

• version 4.4.1 of R or posterior, and
• RStudio, or
• Quarto, or
• Visual Studio Code

R packages

This will be the packages required for the course

install.packages(pkgs = c("sf", "spdep", "lattice", "latticeExtra", "viridis", 
                          "gridExtra", "RColorBrewer", "INLA", "ggthemes", 
                          "leaflet", "ggplot2", "dplyr", "inlabru", "rnaturalearth", 
                          "patchwork"))

The R-INLA package can be downloaded directly from the webpage https://www.r-inla.org/download-install

### --- INLA --- ###
install.packages("INLA",repos=c(getOption("repos"),INLA="https://inla.r-inla-download.org/R/stable"), dep=TRUE)

Also, other packages from Bioconductor

BiocManager::install(c("graph", "Rgraphviz"), dep=TRUE)