Empirical Bayes for geostatistical models

[Sébastien Coube]

Hello, 

Do you have some insight on how much we lose in terms of prediction and estimation when using an Empirical Bayes approach instead of full INLA/MCMC/whatever in a geostatistical model ? 

I think the answer to be "yes" with data sets that give some significant freedom to the posterior distribution for the SPDE/covariance parameters. Håvard and L Held's disease mapping papers identified and addressed the issue of the coupling of the latent field and the high-level parameters. Do you confirm this lead ?

However, with large data sets that should give very slim posterior distributions, do you think that there is a need for full exploration in order to predict and estimate correctly the spatial effects and the effects of covariates ?

Thanks in advance

Sébastien

[Helpdesk (Haavard Rue)]

From the philosifical point of view, 'empirical bayes' is pretty bad or
maybe close to as bad as it can get, as the 'implicite prior' is a point
mass at the mode and all uncertainty are ignored. Variational Bayes is
not even defined for this...

its is very handy if your model contains critical parameters which are
influencial for the model, like the tail-index/parameter for extremes.
including the uncertainty can make a huge impact for predictions, so if
you ignore it, it will be an easier sell... well, that was a joke, but I
think this is the way many sees it, without saying it clearly.

the additional cost of not doing 'eb' is quite moderate, so there is
less to gain computationally these days

if the uncertaintay is small, there is little difference, which can
justufy using 'eb' but there are no formal justifcation in general

H

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Håvard Rue
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[Sébastien Coube]

Thank you Haavard !

Seb