Statistics Seminar: Robustness, Model Checking and Hierarchical Models

Presenter: Rafael Cabral, Member of Technical Staff, Axiom Math

Description: Latent Gaussian models (LGMs) are among the most widely used classes of statistical models, with applications ranging from biostatistics to spatial modeling. Their central assumption, that the latent variables are Gaussian, is nevertheless rarely checked. Many datasets contain sudden jumps or local spikes that a Gaussian latent process over-smooths, impacting both inference and prediction. This talk presents a two-step workflow for hierarchical models, in the spirit of George Box’s loop: model criticism, to check whether the latent assumptions hold, followed by robustification, to fit a more flexible model when they do not. In the criticism step, diagnostic statistics are derived rather than chosen ad hoc, by targeting the departures from Gaussianity induced by a more flexible alternative model. This connects Bayesian predictive checking with robustness analysis and yields a general recipe for assessing latent assumptions, and their impact on the results. In the robustification step, latent non-Gaussian models are fitted using variational Bayes and Laplace approximations. The resulting algorithm iteratively refits LGMs that downweight extreme events in the latent process, giving robust inferences at a fraction of the cost of MCMC. Both steps are implemented in Stan and R-INLA and illustrated with longitudinal, areal and geostatistical applications.

About the speaker: Rafael Cabral is a Member of Technical Staff at Axiom Math in Palo Alto, where he develops AI systems for mathematics and verified reasoning. He received his PhD in Statistics from KAUST in 2023, advised by Håvard Rue and David Bolin, where he worked on model criticism and robust inference for latent Gaussian models. He was subsequently a Research Fellow at the National University of Singapore and a Staff Engineer at Huawei, working on AI safety and reliability. His research interests span Bayesian modeling, robustness, and the application of language models to mathematics and formal reasoning.

This seminar is hosted by Professor Yunyi Shen.