#136 Bayesian Inference at Scale: Unveiling INLA, with Haavard Rue & Janet van Niekerk

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Jul 9, 2025

Haavard Rue, a professor and the mastermind behind Integrated Nested Laplace Approximations (INLA), joins Janet van Niekerk, a research scientist specializing in its application to medical statistics. They dive into the advantages of INLA over traditional MCMC methods, highlighting its efficiency with large datasets. The conversation touches on computational challenges, the significance of carefully chosen priors, and the potential of integrating GPUs for future advancements. They also share insights on using INLA for complex models, particularly in healthcare and spatial analysis.

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ANECDOTE

Janet's INLA Journey Begins

Janet van Niekerk joined Haavard Rue's research group after reaching out post-PhD, starting her journey with INLA.
She initially struggled to understand latent Gaussian models but grew deeply involved in INLA applications and development.

INSIGHT

INLA vs MCMC Explained

INLA uses deterministic mathematical approximations for Bayesian posteriors, avoiding sampling like MCMC.
This leads to much faster computation while still providing credible intervals and means from the posterior.

INSIGHT

Latent Gaussian Models Fit INLA

INLA is specifically designed for latent Gaussian models where model effects have joint Gaussian priors.
This covers a broad class including GAMs, random effects, time series, survival, and spatial models.

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Takeaways:

INLA is a fast, deterministic method for Bayesian inference.
INLA is particularly useful for large datasets and complex models.
The R INLA package is widely used for implementing INLA methodology.
INLA has been applied in various fields, including epidemiology and air quality control.
Computational challenges in INLA are minimal compared to MCMC methods.
The Smart Gradient method enhances the efficiency of INLA.
INLA can handle various likelihoods, not just Gaussian.
SPDs allow for more efficient computations in spatial modeling.
The new INLA methodology scales better for large datasets, especially in medical imaging.
Priors in Bayesian models can significantly impact the results and should be chosen carefully.
Penalized complexity priors (PC priors) help prevent overfitting in models.
Understanding the underlying mathematics of priors is crucial for effective modeling.
The integration of GPUs in computational methods is a key future direction for INLA.
The development of new sparse solvers is essential for handling larger models efficiently.

Chapters:

06:06 Understanding INLA: A Comparison with MCMC

08:46 Applications of INLA in Real-World Scenarios

11:58 Latent Gaussian Models and Their Importance

15:12 Impactful Applications of INLA in Health and Environment

18:09 Computational Challenges and Solutions in INLA

21:06 Stochastic Partial Differential Equations in Spatial Modeling

23:55 Future Directions and Innovations in INLA

39:51 Exploring Stochastic Differential Equations

43:02 Advancements in INLA Methodology

50:40 Getting Started with INLA

56:25 Understanding Priors in Bayesian Models

Thank you to my Patrons for making this episode possible!

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Links from the show:

R-INLA webpage: https://www.r-inla.org/
R-INLA discussion group: https://groups.google.com/g/r-inla-discussion-group
Haavard’s page: https://cemse.kaust.edu.sa/profiles/haavard-rue
Haavard on Google Scholar: https://scholar.google.co.uk/citations?user=VJOn_ZkAAAAJ&hl=en
Janet’s page: https://cemse.kaust.edu.sa/profiles/janet-van-niekerk
Janet on LinkedIn: https://www.linkedin.com/in/janet-van-niekerk-b1803b8a/
Janet on Google Scholar: https://scholar.google.com/citations?user=rZOmGkAAAAAJ&hl=en
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (original and classic formulation): https://users.wpi.edu/~balnan/INLAjrssB2009.pdf
A new avenue for Bayesian inference with INLA (modern formulation of INLA and the current default in the R-INLA package): https://www.sciencedirect.com/science/article/pii/S0167947323000038
Smart Gradient - An adaptive technique for improving gradient estimation: https://www.aimsciences.org/article/doi/10.3934/fods.2021037

SPDE-INLA book and other resources:

Penalizing complexity priors:

Penalizing Model Component Complexity: A Principled, Practical Approach to Constructing Priors: https://doi.org/10.1214/16-STS576
AR processes https://doi.org/10.1111/jtsa.12242
Gaussian fields https://doi.org/10.1080/01621459.2017.1415907
Skew-normal model https://doi.org/10.57805/revstat.v19i1.328
Weibull model https://doi.org/10.1016/j.spl.2021.109098
Splines https://arxiv.org/abs/1511.05748
Many more available in the R-INLA library: inla.pc

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