excursions (version 2.0.6)

continuous: Calculate continuous domain excursion and credible contour sets

Description

Calculates continuous domain excursion and credible contour sets

Usage

continuous(ex, geometry, alpha,
           method = c("log", "logit", "linear", "step"),
           output = c("sp", "inla"))

Arguments

ex

An excurobj object generated by a call to excursions or contourmap.

geometry

Specification of the lattice or triangulation geometry of the input. One of list(x, y), list(loc, dims), inla.mesh.lattice, or inla.mesh, where x and y are vectors, loc

alpha

The target error probability. A warning is given if it is detected that the information ex isn't sufficient for the given alpha. Defaults to the value used when calculating ex

method

The spatial probability interpolation transformation method to use. One of log, logit, linear, or step. For log and logit, the probabilities are interpolated linearly in

output

Specifies what type of object should be generated. sp gives a SpatialPolygons object, and inla gives a inla.mesh.segment object.

Value

• A list:
• M
  SpatialPolygons or inla.mesh.segment object.

  The subsets are tagged, so that credible regions are tagged "-1", and regions between levels are tagged as.character(0:nlevels).

• F
  Interpolated F function
• G
  Contour and inter-level set indices for the interpolation
• F.geometry
  Mesh geometry for the interpolation
• P0
  P0 measure based on interpolated F function (only for contourmap input)

Examples

if (require(INLA)) {
  #Generate mesh and SPDE model
  n.lattice = 10 #Increase for more interesting, but slower, examples
  x=seq(from=0,to=10,length.out=n.lattice)
  lattice=inla.mesh.lattice(x=x,y=x)
  mesh=inla.mesh.create(lattice=lattice, extend=FALSE, refine=FALSE)
  spde <- inla.spde2.matern(mesh, alpha=2)

  #Generate an artificial sample
  sigma2.e = 0.01
  n.obs=100
  obs.loc = cbind(runif(n.obs)*diff(range(x))+min(x),
                  runif(n.obs)*diff(range(x))+min(x))
  Q = inla.spde2.precision(spde, theta=c(log(sqrt(0.5)), log(sqrt(1))))
  x = inla.qsample(Q=Q)
  A = inla.spde.make.A(mesh=mesh,loc=obs.loc)
  Y = as.vector(A %*% x + rnorm(n.obs)*sqrt(sigma2.e))

  ## Calculate posterior
  Q.post = (Q + (t(A)%*%A)/sigma2.e)
  mu.post = as.vector(solve(Q.post,(t(A)%*%Y)/sigma2.e))
  vars.post = excursions.variances(chol(Q.post))

  ## Calculate contour map with two levels
  map = contourmap(n.levels = 2, mu = mu.post, Q = Q.post,
                   alpha=0.1, F.limit = 0.1)

  ## Calculate the continuous representation
  sets <- continuous(map, mesh, alpha=0.1)

  ## Plot the results
  reo = mesh$idx$lattice
  cols = contourmap.colors(map, col=heat.colors(100, 1),
                           credible.col = grey(0.5, 1))
  names(cols) = as.character(-1:2)

  par(mfrow = c(2,2))
  image(matrix(mu.post[reo],n.lattice,n.lattice),main="mean",axes=F)
  image(matrix(sqrt(vars.post[reo]),n.lattice,n.lattice),main="sd", axes = F)
  image(matrix(map$M[reo],n.lattice,n.lattice),col=cols,axes=F)
  idx.M = setdiff(names(sets$M), "-1")
  plot(sets$M[idx.M], col=cols[idx.M])
}