PIPELINE FOR BUILD BARRIER INLA MODELS - PROBLEMS WITH COMPUTING BARRIERS

[Lola Riesgo Torres]

Hi everyone,
I am trying to build a spatial model accounting for barriers. However, I do not fully understand the pipeline (workflow) we are supposed to follow. I have only found three available tutorials on implementing a barrier model, but I am confused about why they differ. The tutorials are:

1. https://eliaskrainski.github.io/INLAspacetime/articles/web/barrierExample.html#abstract

2. https://haakonbakkagit.github.io/btopic128.html#6_Implementation_(Models) (obsolete)

3. https://becarioprecario.bitbucket.io/spde-gitbook/ch-nonstationarity.html#ch:barrier

What I don’t understand is how they create the s.index after defining the SPDE. In a model without barriers, the steps are:

A) Define the mesh
B) Define the SPDE (inla.spde2.pcmatern) and create the s-index (inla.spde.make.index)

spde <- inla.spde2.pcmatern(mesh, prior.range = c(1, 0.01), prior.sigma = c(1, 0.01))
s.index <- inla.spde.make.index(name = "spatial.field", n.spde = spde$n.spde)

C) Define the projection matrix A (inla.spde.make.A)
D) Define the stack (here you introduce the s.index)  

For example:
stack.1 <- inla.stack(
  data   = list(y = df$pres),
  A      = list(A, 1),
  effects = list(
    s.index,  
    df %>% transmute(
      intercept = 1,
      temp_s, time, bathy_s, length_cm_s
    )
  ),
  tag = "fit"
)

E) Define the formula and fit the model  

For example: 

f.1 <- y ~ -1 +intercept + bathy_s + temp_s + f(spatial.field, model = spde)

mod.1 <- inla(
  f.1,
  data              = inla.stack.data(stack.1),
  family            = "binomial",
  control.predictor = list(
    A       = inla.stack.A(stack.1),
    compute = TRUE
  ),
  control.compute   = list(dic = TRUE, waic = TRUE, cpo = TRUE),
  verbose           = TRUE
)

However, in the barrier model the workflow seems different. In the tutorials, they do not define a s.index. The workflow is:

A) Define the mesh accounting for the boundary (water polygon)
B) Identify the triangles inside the polygon (fmesher::fm_contains)
C) Create a SPDE with the barrier (inla.barrier.pcmatern) – here no s.index is define

For example: 

water.tri <- fmesher::fm_contains(
  ocean_poly,
  y = mesh,
  type = "centroid"
)

water.tri.idx <- water.tri[[1]]
length(water.tri.idx)  
num.tri <- nrow(mesh$graph$tv)
barrier.tri <- setdiff(1:num.tri, water.tri.idx)

poly.barrier <- inla.barrier.polygon(
  mesh,
  barrier.triangles = barrier.tri
)

spde_barrier <- inla.barrier.pcmatern(
  mesh = mesh,
  barrier.triangles = barrier.tri,
  prior.range = c(100000, 0.5),
  prior.sigma = c(1, 0.01)
)

D) Build the projection matrix A
E) Define the stack – where in the previous method you have s.index, here the code uses s = 1:mesh$n. For example:

stack.1 <- inla.stack(
  data   = list(y = df$presence),
  A      = list(A, 1),
  effects = list(
    s= 1:mesh$n,  
    df %>% transmute(
      intercept = 1,
      Depth_s, BotTemp_s, year_f, mean_len_s
    )
  ),
  tag = "fit"
)

F) Define the formula and fit the model with INLA

The problem is that when I apply this workflow, the spatial effect does not seem to be used. My question is: do I need to define SPDE indices (s.index) in a barrier model? If not, why does INLA not seem to include the spatial effect?  

Thank you so much for the information and help. 

Kind regards, 

Lola R

[Elias T. Krainski]

Dear Lola, 

The first link uses the current recommended implementation, while the others use an old one. Additionally, it uses inlabru, which is why the 's.index' creation is not necessary, as the interface with inla has become easier. 

Best regards, 

Elias

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