Interpreting $summary.hyperpar Output for rSPDE Matérn Models

[Filippo Rambelli]

Dear R-INLA community,

I would like to ask for your help in interpreting the output of $summary.hyperpar.

Because of the smoothness constraint in inla.spde2.matern() (nu can only be ≤ 1 in the 2D case), I am using rspde.matern() to define an spde matern model with fixed smoothness 1.5 (see inla.spde2.matern() smoothness). 

The model fitted with inla() returns $summary.hyperpar, which corresponds to range and standard deviation when parameterization = "matern", and to kappa and tau when parameterization = "spde"

The hyperparameter estimates appear to be transformed, as the posterior means of kappa or the standard deviation can be negative. This seems to be in line with the discussion in Re: [r-inla] Variability explained where it is mentioned that "Theta1 and theta2 are the internal parameterisation of the “humanly interpretable” parameter". 

Finn Lindgren suggested using inla.spde2.result() to convert the results, but this does not seem to be compatible with SPDE objects defined via rSPDE.

How can we manually convert the estimates shown in $summary.hyperpar into the humanly interpretable values for both parameterizations?
The code is attached.

Thank you in advance,

Filippo

[Helpdesk (Haavard Rue)]

https://davidbolin.github.io/rSPDE/articles/rspde_inla.html#inla-results

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Håvard Rue
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