Hi everyone,
We (@javier.aguilar , @eyanchenko , Shonosuke Sugasawa, Kaoru Irie, @avehtari , and @paul.buerkner ) have a new preprint on incorporating structural domain knowledge—such as heredity between main effects and interactions, preferring linear over spline basis terms in GAMs, or ordering effect magnitudes—into shrinkage priors.
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Preprint: [2610.38879] Proximal R2 Priors for Structured Variance Allocation
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Code & Stan models: GitHub - davkoh/prox-r2: Proximal R2D2 Priors for Structured Variance Allocation · GitHub
In regressions with structured terms, we often want to favour a specific variance hierarchy without enforcing it strictly. Building on the R^2 decomposition framework, we introduce the Prox-R2 prior, which encodes these structural preferences as linear inequality constraints on variance allocations and relaxes them via their Moreau–Yosida envelope into a smooth distance penalty. Notably, this allows us to use Stan directly for proximal MCMC: the projection and penalty are computed right inside the Stan model, yielding a continuously differentiable target that samples out of the box with HMC/NUTS while guarding against structural misspecification.
Theoretically, we prove that Prox-R2 preserves many of the niceties one expects from shrinkage priors.
All Stan models and replication code are available in our repo ( GitHub - davkoh/prox-r2: Proximal R2D2 Priors for Structured Variance Allocation · GitHub ). Feedback and questions are very welcome!