Transferability with INLA models

[Lola Riesgo Torres]

Hi everyone,

I have been using INLA for some time, mainly to build Species Distribution Models for data-poor species (i.e., with small sample sizes). I would like to ask about the community’s experience with predicting in areas outside the inference domain.

In the case of data-poor species, the spatial random effect often plays a major role in model predictions, as it tends to absorb much of the unexplained variation. However, this spatial effect is intrinsically linked to the locations of the sampling points. When predicting outside the inference area, these sampling locations are no longer present, meaning that the spatial structure may not be well supported.

Given this, would you say that models with strong spatial random effects are more suitable for inference within the sampled domain rather than for extrapolation to new areas? I would be very interested to hear about your experiences or your thoughts about it...

Also, I understand that in theory it is possible to break down the spatial effect to assess the extent to which it is capturing variation that could be attributed to environmental covariates, so may be this could help to predict beyond the mesh?

Thank you so much in advance for taking your time to write a response!! :)

Lola Riesgo

[Finn Lindgren]

Hi,

when applying an estimated model to a new region, the spatial random effect field (for a stationary model) results in a pointwise increase in the prediction uncertainty (with some spatial correlation).

Whether that's useful or not will be context dependent; of course it also depends on whether other aspects of the new region is sufficiently similar to the one used for estimation.

In some cases, the spatial effect captures local variability, which may be similar in a new region. In other cases, it captures otherwise unmodelled systematic differences from what can be explained by the available covariates.

In the latter case, there isn't much one can do other than improve the model with new data/covariates. In the first case, the induced uncertainty may be precisely what is needed for prediction with appropriate uncertainty.

Which case one is in isn't determined by the model definition, but rather how the real world actually behaves when comparing two regions, so which situation you're in is something you need problem specific expertise to determine.

Finn

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Finn Lindgren
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