Andy Seaton
@aseaton.bsky.social
Unemployed and chronically ill statistician. Convalescing and writing and hoping for health to return.
Have you seen this beast: arxiv.org/abs/2402.07084
I read it a bit a few years ago but have never gone through it in detail. Just a brief 180 pages...
I read it a bit a few years ago but have never gone through it in detail. Just a brief 180 pages...
Reproducing kernel methods for machine learning, PDEs, and statistics
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and nume...
arxiv.org
January 15, 2026 at 12:22 AM
Have you seen this beast: arxiv.org/abs/2402.07084
I read it a bit a few years ago but have never gone through it in detail. Just a brief 180 pages...
I read it a bit a few years ago but have never gone through it in detail. Just a brief 180 pages...
Got it, I think I don't understand where a Jacobian would come into it but I should probably just go and read the docs.
January 14, 2026 at 5:36 PM
Got it, I think I don't understand where a Jacobian would come into it but I should probably just go and read the docs.
I am fond of this perspective since it was my way into the literature in the first place. I started with INLA, then the SPDE approach, then Dave Miller convinced me to try and recreate it in mgcv. It was a very informative exercise for me.
January 14, 2026 at 5:35 PM
I am fond of this perspective since it was my way into the literature in the first place. I started with INLA, then the SPDE approach, then Dave Miller convinced me to try and recreate it in mgcv. It was a very informative exercise for me.
But I'm not sure I've seen any systematic discussion of situations like this.
January 14, 2026 at 5:30 PM
But I'm not sure I've seen any systematic discussion of situations like this.
I think I've seen stuff like
1. Don't define the mesh where the animal wont go (not a great idea if you are wanting to infer species-habitat associations...)
2. Include a factor covariate and hope the estimate is strongly significant so an apparent hard threshold appears in the predicted intensity
1. Don't define the mesh where the animal wont go (not a great idea if you are wanting to infer species-habitat associations...)
2. Include a factor covariate and hope the estimate is strongly significant so an apparent hard threshold appears in the predicted intensity
January 14, 2026 at 5:30 PM
I think I've seen stuff like
1. Don't define the mesh where the animal wont go (not a great idea if you are wanting to infer species-habitat associations...)
2. Include a factor covariate and hope the estimate is strongly significant so an apparent hard threshold appears in the predicted intensity
1. Don't define the mesh where the animal wont go (not a great idea if you are wanting to infer species-habitat associations...)
2. Include a factor covariate and hope the estimate is strongly significant so an apparent hard threshold appears in the predicted intensity
Also thanks for taking the time to reply. It's fun being online again and talking stats. I've been out of the game for 3+ years for health reasons, so I appreciate it a lot!
January 14, 2026 at 5:25 PM
Also thanks for taking the time to reply. It's fun being online again and talking stats. I've been out of the game for 3+ years for health reasons, so I appreciate it a lot!
Got it, will keep this in mind. Hard to know how much I will be allowed to harp on about this stuff in our paper but I would like to get something in there if possible.
January 14, 2026 at 5:23 PM
Got it, will keep this in mind. Hard to know how much I will be allowed to harp on about this stuff in our paper but I would like to get something in there if possible.
Are people in fisheries doing spline stuff in constrained parameter domains where they need a transformation to something that plays well with stan? Don't know much about stan or fisheries.
January 14, 2026 at 5:22 PM
Are people in fisheries doing spline stuff in constrained parameter domains where they need a transformation to something that plays well with stan? Don't know much about stan or fisheries.
I also have strong opinions! Then I look at what mgcv does and what, e.g., INLA does and I go ach it's not so different really. Thinking about it properly feels really important, but it in many cases it may not lead to anything consequentially different in terms of inference...
January 14, 2026 at 5:14 PM
I also have strong opinions! Then I look at what mgcv does and what, e.g., INLA does and I go ach it's not so different really. Thinking about it properly feels really important, but it in many cases it may not lead to anything consequentially different in terms of inference...
Thanks, I will have a read. The title alone it reads like something I want to say is not quite true! But it's so useful to act like it's true when learning about the methods, especially if someone is already familiar with GPs or splines.
January 14, 2026 at 2:59 PM
Thanks, I will have a read. The title alone it reads like something I want to say is not quite true! But it's so useful to act like it's true when learning about the methods, especially if someone is already familiar with GPs or splines.
I think the thing I'm handwringing over is that there is a mathematical connection between the two approaches, but the bridge between the two inference paradigms is quite narrow, and an important part of inference (uncertainty around point estimates) is conspicuously absent from that connection.
January 14, 2026 at 2:57 PM
I think the thing I'm handwringing over is that there is a mathematical connection between the two approaches, but the bridge between the two inference paradigms is quite narrow, and an important part of inference (uncertainty around point estimates) is conspicuously absent from that connection.
Again, another messy discussion I am not sure we need to or want to get into, but amounts to a discussion of 'what is the difference between an inhomogeneous Poisson process and a Cox process' and how splines fit into that conversation.
January 14, 2026 at 2:51 PM
Again, another messy discussion I am not sure we need to or want to get into, but amounts to a discussion of 'what is the difference between an inhomogeneous Poisson process and a Cox process' and how splines fit into that conversation.
Unfortunately such a neat presentation doesn't quite work for us because we are using splines in a point process model. So the interpretation of a spline component can vary and often relates to a philosophical statement 'what would I think if I saw another realisation of the point process'.
January 14, 2026 at 2:51 PM
Unfortunately such a neat presentation doesn't quite work for us because we are using splines in a point process model. So the interpretation of a spline component can vary and often relates to a philosophical statement 'what would I think if I saw another realisation of the point process'.
I feel like I'm twisting myself in knots. I care about this. But I don't know if it matters. Would be interested if anyone has any thoughts.
Anyway, after the pain of copying and pasting this into bluesky I think I am learning why people write blog posts instead of doing this nonsense.
Anyway, after the pain of copying and pasting this into bluesky I think I am learning why people write blog posts instead of doing this nonsense.
January 14, 2026 at 2:38 PM
I feel like I'm twisting myself in knots. I care about this. But I don't know if it matters. Would be interested if anyone has any thoughts.
Anyway, after the pain of copying and pasting this into bluesky I think I am learning why people write blog posts instead of doing this nonsense.
Anyway, after the pain of copying and pasting this into bluesky I think I am learning why people write blog posts instead of doing this nonsense.
inference is about a lot more than posterior means and point estimates."
(here endeth the quote from my email, with some minor edits for clarity)
(here endeth the quote from my email, with some minor edits for clarity)
January 14, 2026 at 2:38 PM
inference is about a lot more than posterior means and point estimates."
(here endeth the quote from my email, with some minor edits for clarity)
(here endeth the quote from my email, with some minor edits for clarity)
saying "penalties = priors" seems like a good enough rule of thumb, but then from other perspectives you want to say "okay penalties and priors aren't actually the same thing because the equivalence is only between a point estimate and a posterior mean and
January 14, 2026 at 2:38 PM
saying "penalties = priors" seems like a good enough rule of thumb, but then from other perspectives you want to say "okay penalties and priors aren't actually the same thing because the equivalence is only between a point estimate and a posterior mean and
That being said, what something like mgcv does to generate confidence intervals for spline estimators is something that, using large sample justifications for the approximations, looks like an approximation to a Bayesian posterior.
So it's this awful grey area where
So it's this awful grey area where
January 14, 2026 at 2:38 PM
That being said, what something like mgcv does to generate confidence intervals for spline estimators is something that, using large sample justifications for the approximations, looks like an approximation to a Bayesian posterior.
So it's this awful grey area where
So it's this awful grey area where
Unless you want to claim that Bayesian inference amounts to only inferring a posterior mean, or that we should call penalties priors when we do frequentis-based inference.
January 14, 2026 at 2:38 PM
Unless you want to claim that Bayesian inference amounts to only inferring a posterior mean, or that we should call penalties priors when we do frequentis-based inference.
While it is true that, in the Bayesian version, the prior looks like the penalty, in the form of a Gaussian prior with a particular (possibly not-full rank) precision matrix, it is not true that the penalty and the prior are the same thing.
January 14, 2026 at 2:38 PM
While it is true that, in the Bayesian version, the prior looks like the penalty, in the form of a Gaussian prior with a particular (possibly not-full rank) precision matrix, it is not true that the penalty and the prior are the same thing.
The optimal penalised smoothing spline (the thing that maximises the penalised likelihood) is the same as the posterior mean under a specific Bayesian formulation of the model.
January 14, 2026 at 2:38 PM
The optimal penalised smoothing spline (the thing that maximises the penalised likelihood) is the same as the posterior mean under a specific Bayesian formulation of the model.
(On discussing some papers that make 'penalties = priors' handwavey statements)
"But they don't get to the crux of the matter which is the following result proved sometime in the 70s by Wahba and Kimeldorf (and maybe others I forget the names now):
"But they don't get to the crux of the matter which is the following result proved sometime in the 70s by Wahba and Kimeldorf (and maybe others I forget the names now):
Client Challenge
link.springer.com
January 14, 2026 at 2:38 PM
(On discussing some papers that make 'penalties = priors' handwavey statements)
"But they don't get to the crux of the matter which is the following result proved sometime in the 70s by Wahba and Kimeldorf (and maybe others I forget the names now):
"But they don't get to the crux of the matter which is the following result proved sometime in the 70s by Wahba and Kimeldorf (and maybe others I forget the names now):
January 14, 2026 at 2:38 PM
And thus it was decreed that all students of introduction to probability will have to also think about balls in urns.
January 7, 2026 at 6:13 PM
And thus it was decreed that all students of introduction to probability will have to also think about balls in urns.