Non stationary mean in SPDE

[Nafsika Antoniadou]

Hello,

Can the spatial random effect have a spatially non-stationary mean (instead of 0), or does that mess with the SPDE approximation?  

Thanks a lot

[Finn Lindgren]

It’s not a problem in theory, but I don’t think the interface has a way to do it.

One can always rewrite it as a sum of a non random function and a zero mean process, and you can explicitly write it like that in inlabru predictors, by adding the effect of the random field to a constant value (i.e. no random, with model=“const”).

It would be possible to add a “shift” feature to inlabru components that would accomplish this; there is already a bm_shift() mapper, and the component weights are implemented using a bm_scale() mapper, so this could work the same way, so both scaling and shifts would be incorporated into the effect of the component.

Might be worth explaining what your use case is.

Finn

On 9 Oct 2025, at 14:26, Nafsika Antoniadou <antoniadou...@gmail.com> wrote:



Hello,

Can the spatial random effect have a spatially non-stationary mean (instead of 0), or does that mess with the SPDE approximation?  

Thanks a lot

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[Finn Lindgren]

In my proposed feature, I miswrote; there are two possibilities that are both useful; to apply a known shift to the latent variables directly, and to apply a shift to the _effect_ of the component. The former operates on the latent variables directly, and the latter operates on the predictor expression. But adding known values to the predictor is already supported, so the added usefulness of associating it with specific components is less than shifting the latent variables.

Finn

On 9 Oct 2025, at 14:49, Finn Lindgren <finn.l...@gmail.com> wrote:

It’s not a problem in theory, but I don’t think the interface has a way to do it.