excursions (version 2.0.6)

excursions.inla: Excursion sets and contour credible regions for latent Gaussian models

Description

Excursion sets and contour credible regions for latent Gaussian models calculated using the INLA method.

Usage

excursions.inla(result.inla,
                stack,
                name=NULL,
                tag=NULL,
                ind=NULL,
                method,
                alpha=1,
                F.limit,
                u,
                u.link = FALSE,
                type,
                n.iter=10000,
                verbose=0,
                max.threads=0,
                seed=NULL)

Arguments

result.inla

Result object from INLA call

stack

The stack object used in the INLA call.

tag

The tag of the component in the stack for which to do the calculation. This argument should only be used if a stack object is provided, use the name argument otherwise.

name

The name of the component for which to do the calculation. This argument should only be used if a stack object is not provided, use the tag argument otherwise.

ind

If only a part of a component should be used in the calculations, this argument specifies the indices for that part.

method

Method for handeling the latent Gaussian structure:

• 'EB'

{Empirical Bayes} 'QC'{Quantile correction} 'NI'{Numerical integration} 'NIQC'{Numerical integration with quantile corre

Value

• excursions.inla returns an object of class "excurobj". This is a list that contains the following arguments:
• E
  Excursion set, contour credible region, or contour avoiding set
• F
  The excursion function corresponding to the set E calculated for values up to F.limit
• G
  Contour map set. $G=1$ for all nodes where the $mu > u$.
• M
  Contour avoiding set. $M=-1$ for all non-significant nodes. $M=0$ for nodes where the process is significantly below u and $M=1$ for all nodes where the field is significantly above u. Which values that should be present depends on what type of set that is calculated.
• rho
  Marginal excursion probabilities
• mean
  Posterior mean
• vars
  Marginal variances
• meta
  A list containing various information about the calculation.

item

• alpha
• F.limit
• u
• u.link
• type
• '<'< li="">
• '!='
• '='
• n.iter
• verbose
• max.threads
• seed

code

u

itemize

• '>'

References

Bolin, D. and Lindgren, F. (2015) Excursion and contour uncertainty regions for latent Gaussian models, JRSS-series B, vol 77, no 1, pp 85-106.

Examples

## In this example, we calculate the excursion function
## for a partially observed AR process.
if (require(INLA)) {
## Sample the process:
rho = 0.9
tau = 15
tau.e = 1
n = 100
x = 1:n
mu = 10*((x<n/2)*(x-n/2) + (x>=n/2)*(n/2-x)+n/4)/n
Q = tau*sparseMatrix(i=c(1:n, 2:n), j=c(1:n, 1:(n-1)),
                   x=c(1,rep(1+rho^2, n-2),1, rep(-rho, n-1)),
                   dims=c(n, n), symmetric=TRUE)
X = mu+solve(chol(Q), rnorm(n))

## measure the sampled process at n.obs random locations
## under Gaussian measurement noise.
n.obs = 50
obs.loc = sample(1:n,n.obs)
A = sparseMatrix(i=1:n.obs, j=obs.loc, x=rep(1, n.obs), dims=c(n.obs, n))
Y = as.vector(A %*% X + rnorm(n.obs)/sqrt(tau.e))

## Estimate the parameters using INLA
ef = list(c(list(ar=x),list(cov=mu)))
s.obs = inla.stack(data=list(y=Y), A=list(A), effects=ef, tag="obs")
s.pre = inla.stack(data=list(y=NA), A=list(1), effects=ef,tag="pred")
stack = inla.stack(s.obs,s.pre)
formula = y ~ -1 + cov + f(ar,model="ar1")
result = inla(formula=formula, family="normal", data = inla.stack.data(stack),
              control.predictor=list(A=inla.stack.A(stack),compute=TRUE),
              control.compute = list(config = TRUE))

## calculate the level 0 positive excursion function
res.qc =
excursions.inla(result, stack = stack, tag = 'pred', alpha=0.99, u=0,
                method='QC', type='>', max.threads=2)

## plot the excursion function and marginal probabilities
plot(res.qc$rho,type="l",
     main="marginal probabilities (black) and excursion function (red)")
lines(res.qc$F,col=2)
}