Interpreting Theta from barrier models

[KB]

Hi,

I am fitting a barrier model in INLA with the following code: 

spde1 <- inla.barrier.pcmatern(mesh,barrier.triangles = barrier_tri,

                             prior.range = c(20, 0.5),
                             prior.sigma = c(1, 0.5))

I noticed that in the model hyperparameter output, these models report Theta1 for s and Theta2 for s instead of Range for s and stdev for s.

The Krainski et al. (2019) INLA-SPDE book in the Barrier Model chapter reports on page 167, that the order are reversed in the barrier models, indicating that 

σ=eθ1is the marginal standard deviationr=eθ2is the spatial range

My model output is below:

Model hyperparameters:
                               mean    sd     0.025quant 0.5quant   0.975quant    mode
Theta1 for s       3.956 0.088      3.786         3.955               4.132            3.952
Theta2 for s       0.678 0.073      0.536          0.677              0.822            0.674

Does this indicate that if I calculate exp(3.956), then I will obtain the sd and exp(0.678) will be the range in the same units as the coordinates I used to make the mesh?  

Also, I noticed that Theta1 and Theta2 do not change much depending upon the priors I use in my code above. I just want to make sure, if specifying the priors as I have done is the same for when inla.spde2.pcmatern is used versus inla.barrier.pcmatern.

Thanks so much.

[Elias T. Krainski]

Hi, 

Please have a look at the tutorial at https://eliaskrainski.github.io/INLAspacetime/articles/web/barrierExample.html where it is about the re-implementation of this model. The priors are the same as for the stationary model.

Elias

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