Gavin Simpson
gsimpson.bsky.social
Gavin Simpson
@gsimpson.bsky.social
(Palaeo)[ecologist | limnologist] & #fakeStatistican, #rstats user, wielder of #GAMs. He/him/his. Opinions mine…
I’d start with Dave Miller’s recent paper on the Bayesian Interpretation of GAMs in MEE arxiv.org/abs/1902.01330

The equivalence holds for the case of a Bayesian view of smoothing as that looks like the REML criterion of a mixed effects model
Bayesian views of generalized additive modelling
Generalized additive models (GAMs) are a commonly used, flexible framework applied to many problems in statistical ecology. GAMs are often considered to be a purely frequentist framework (`generalized...
arxiv.org
January 15, 2026 at 7:52 AM
If this is a general “penalties = priors” thing I don’t think that is generally true. There are specific cases where they work out to be equivalent to a particular (possibly improper) prior. This is what underlies mgcv and IIRC also INLA (but I’m less familiar with the latter)
January 15, 2026 at 7:46 AM
I think that would be using an “old style” or “scheffer style” random effect interpretation sensu Hodges. We don’t tend to think our spline is a draw from a multivariate Gaussian as if it were some weird set of random effects but we use this as a computational convenience, AKA “new style” ranefs
January 15, 2026 at 7:40 AM
Isn’t this called maximum a posteriori estimation? What mgcv does is an empirical Bayesian edtimate. The “penalty” is an improper Gaussian prior on the smooth coefs and lambda is inversely proportional to a variance parameter. I’m away from my books & other stuff but I think this is in Wood 2011
January 15, 2026 at 7:35 AM
Reposted by Gavin Simpson
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2/2
January 5, 2026 at 11:57 AM
Congratulations Stephen 🎉🍾
December 31, 2025 at 1:22 PM