Be Bayesian my Friend 2.0.

Welcome to the course Be Bayesian my Friend 2.0., a continuation of the short course
Be Bayesian, My Friend.

This is a 20-hour course designed to provide a comprehensive introduction to Bayesian inference, from foundational concepts to modern methodologies such as MCMC, JAGS, stan, brms, INLA and inlabru, including hierarchical and spatial models.

The course combines theory and practice, with real-world examples and hands-on implementations in R.

🧠 Course Overview

The course is structured in four main parts, covering the full Bayesian workflow: from probabilistic reasoning to advanced modeling.

Part I: Foundations of Bayesian Inference (5h)

• Motivation and real-world problems
• Bayesian paradigm: prior, likelihood, posterior
• Bayesian updating
• Conjugate models (Beta–Binomial)
• Predictive distributions

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Part II: Bayesian Computation (5h)

• Monte Carlo methods
• MCMC (Metropolis–Hastings)
• Bayesian software (JAGS, Stan, brms)

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Part III: INLA and Latent Gaussian Models (5h)

• Hierarchical models and mixed effects
• Latent Gaussian models
• INLA methodology and implementation
• Model selection (DIC, WAIC)

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Part IV: Spatial Statistics (5h)

• Types of spatial data
• Disease mapping
• Geostatistics
• Gaussian fields and spatial dependence
• SPDE approach with INLA
• PC priors

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💻 Software Requirements

To follow the practical sessions, please ensure that the following software is installed:

• R (version 4.5.1 or later)
• RStudio or
• Quarto or
• Visual Studio Code
• JAGS

⚠️ Some examples rely on external software such as JAGS.

INLA Installation

The examples use the INLA package version:

This is INLA_25.06.07 built 2025-06-11 18:54:45 UTC; unix.
- See www.r-inla.org/contact-us for how to get help.
- List available models/likelihoods/etc with inla.list.models()
- Use inla.doc(<NAME>) to access documentation
- Consider upgrading R-INLA to testing[25.10.28] or stable[25.10.19]

You can install it directly from the official INLA repository:

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

For more information, visit the official installation guide:
🔗 https://www.r-inla.org/download-install

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📦 R Packages

Install the required packages with:

install.packages(c(
  "INLA", "inlabru", "Matrix", "sp", "sf", "spdep",
  "tmap", "raster", "terra", "ggplot2", "dplyr",
  "readxl", "kableExtra", "runjags", "brms",
  "viridis", "RColorBrewer", "gridExtra",
  "patchwork", "leaflet", "ggthemes", "rnaturalearth"
))

Additional dependencies (Bioconductor)

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

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📁 Folder Structure

The repository is organized as follows:

BAYESIANLEARNING/
│
├── PART-I/
│   ├── theory/
│   │   └── PI_bayesian_inference.pdf
│   └── examples/
│       └── PI-BI_beta_binomial/
│
├── PART-II/
│   ├── theory/
│   │   └── PII_bayesian_computation.pdf
│   ├── examples/
│   └── exercises/
│       └── PII-diabetes/
│
├── PART-III/
│   ├── theory/
│   │   └── PIII_inla.pdf
│   ├── examples/
│   │   ├── PIII-INLA-KAKHI-VALENCIA/
│   │   ├── PIII-INLA-measurement_agreement_COPD/
│   │   ├── PIII-INLA-rain/
│   │   └── PIII-INLA-seeds/
│   └── exercises/
│
├── PART-IV/
│   ├── theory/
│   │   └── PIV_spatial.pdf
│   ├── examples/
│   │   ├── PIV-INLA-disease-mapping/
│   │   ├── PIV-inlabru-geostatistics/
│   │   └── PIV-inlabru-mesh/
│
└── README.md

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📌 Notes

• PART-I: Foundations of Bayesian inference

• PART-II: Computation and hierarchical models (MCMC)

• PART-III: INLA methodology and latent Gaussian models

• PART-IV: Spatial statistics and advanced models

• theory/ contains lecture slides (HTML/PDF)

• examples/ contains worked case studies

• exercises/ contains hands-on practice material

🎯 Learning Outcomes

By the end of this course, participants will be able to:

• Understand Bayesian reasoning and the role of the prior, likelihood, and posterior distributions.
• Build and interpret Bayesian models for real-world problems.
• Implement Bayesian inference using MCMC methods (JAGS, Stan, and brms).
• Apply INLA for fast approximate inference in latent Gaussian models (LGMs).
• Develop hierarchical (mixed) models to capture structured variability.
• Model and interpret spatial data using Bayesian approaches.
• Evaluate models using criteria such as DIC and WAIC.
• Communicate results through posterior summaries, predictions, and uncertainty quantification.

👨‍🏫 Instructor

Joaquín Martínez-Minaya
Applied Statistics and Operations Research and Quality (DEIOAC)
Universitat Politècnica de València (UPV)

📧 Email: [email protected]
🌐 Website: https://github.com/jmartinez-minaya

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📚 Bibliography

1. Bachl, F. E., Lindgren, F., Borchers, D. L., & Illian, J. B. (2019). inlabru: An R package for Bayesian spatial modelling from ecological survey data. Methods in Ecology and Evolution, 10(6), 760–766. https://doi.org/10.1111/2041-210X.13168

2. Blangiardo, M., & Cameletti, M. (2015). Spatial and Spatio-temporal Bayesian Models with R-INLA. Wiley.

3. Broemeling, L. D. (2013). Bayesian Methods in Epidemiology. Chapman and Hall/CRC.

4. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC.

5. Gómez-Rubio, V. (2020). Bayesian Inference with INLA. CRC Press.

6. Krainski, E., Gómez-Rubio, V., Bakka, H., Lenzi, A., Rue, H., & Lindgren, F. (2019). Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA. Chapman and Hall/CRC.

7. Lawson, A. B. (2018). Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology (3rd ed.). CRC Press.

8. Lesaffre, E., & Lawson, A. B. (2012). Bayesian Biostatistics. Chapman & Hall/CRC Biostatistics Series.

9. Martínez-Beneito, M. A., & Botella-Rocamora, P. (2019). Disease Mapping: From Foundations to Multidimensional Modeling. CRC Press.

10. Moraga, P. (2019). Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny. Chapman and Hall/CRC.

11. Moraga, P. (2021). Handbook of Spatial Epidemiology and Disease Modeling: Applications with R. CRC Press.

12. Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations. Journal of the Royal Statistical Society: Series B, 71(2), 319–392.