Old SPDE model objects for INLA

Description

Create an inla.spde1 model object.

Usage

inla.spde1.create(
  mesh,
  model = c("matern", "imatern", "matern.osc"),
  param = NULL,
  ...
)

inla.spde1.matern(mesh, ...)

inla.spde1.imatern(mesh, ...)

inla.spde1.matern.osc(mesh, ...)

Arguments

Details

Note: This is an old spde object format retained for backwards compatibility. Please use inla.spde2() models for new code.

This method constructs an object for SPDE models. Currently implemented:

model="matern"

(kappa^2(u)-Delta)^(alpha/2) (tau(u) x(u)) = W(u)

(kappa^2(u)-Delta)^(alpha/2) (tau(u) x(u)) = W(u)

param:

• alpha = 1 or 2

• basis.T = Matrix of basis functions for log tau(u)

• basis.K = Matrix of basis functions for log kappa^2(u)

model="imatern"

(-Delta)^(alpha/2) (tau(u) x(u)) = W(u)

(-Delta)^(alpha/2) (tau(u) x(u)) = W(u)

param:

• alpha = 1 or 2

• basis.T = Matrix of basis functions for log tau(u)

Value

An inla.spde1 object.

Author(s)

Finn Lindgren finn.lindgren@gmail.com

See Also

inla.spde2.matern(), inla.mesh.2d(), inla.mesh.basis()

Examples

n = 100
field.fcn = function(loc) (10*cos(2*pi*2*(loc[,1]+loc[,2])))
loc = matrix(runif(n*2),n,2)
## One field, 2 observations per location
idx.y = rep(1:n,2)
y = field.fcn(loc[idx.y,]) + rnorm(length(idx.y))

mesh = inla.mesh.create(loc, refine=list(max.edge=0.05))
spde = inla.spde1.create(mesh, model="matern")
data = list(y=y, field=mesh$idx$loc[idx.y])
formula = y ~ -1 + f(field, model=spde)
result = inla(formula, data=data, family="normal")

## Plot the mesh structure:
plot(mesh)

if (require(rgl)) {
  ## Plot the posterior mean:
  plot(mesh, rgl=TRUE,
       result$summary.random$field[,"mean"],
       color.palette = colorRampPalette(c("blue","green","red")))
  ## Plot residual field:
  plot(mesh, rgl=TRUE,
       result$summary.random$field[,"mean"]-field.fcn(mesh$loc),
       color.palette = colorRampPalette(c("blue","green","red")))
}