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Excursion sets and contour credible regions using Monte Carlo samples

Source: R/interface.mc.R
excursions.mc.Rd

excursions.mc is used for calculating excursion sets, contour credible regions, and contour avoiding sets based on Monte Carlo samples of models.

Usage

excursions.mc(
  samples,
  alpha,
  u,
  type,
  rho,
  reo,
  ind,
  max.size,
  verbose = FALSE,
  prune.ind = FALSE
)

Arguments

samples

Matrix with model Monte Carlo samples. Each column contains a sample of the model.

alpha

Error probability for the excursion set.

u

Excursion or contour level.

type

Type of region:

'>'

positive excursions

'<'

negative excursions

'!='

contour avoiding function

'='

contour credibility function

rho

Marginal excursion probabilities (optional). For contour regions, provide \(P(X>u)\).

reo

Reordering (optional).

ind

Indices of the nodes that should be analysed (optional).

max.size

Maximum number of nodes to include in the set of interest (optional).

verbose

Set to TRUE for verbose mode (optional).

prune.ind

If TRUE and ind is supplied, then the result object is pruned to contain only the active nodes specified by ind.

Value

excursions.mc returns an object of class "excurobj" with the following elements

E

Excursion set, contour credible region, or contour avoiding set.

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.

F

The excursion function corresponding to the set E calculated for values up to F.limit

rho

Marginal excursion probabilities

mean

The mean mu.

vars

Marginal variances.

meta

A list containing various information about the calculation.

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.

Bolin, D. and Lindgren, F. (2018), Calculating Probabilistic Excursion Sets and Related Quantities Using excursions, Journal of Statistical Software, vol 86, no 1, pp 1-20.

See also

excursions(), excursions.inla()

Author

David Bolin davidbolin@gmail.com and Finn Lindgren finn.lindgren@gmail.com

Examples

## Create mean and a tridiagonal precision matrix
n <- 101
mu.x <- seq(-5, 5, length = n)
Q.x <- Matrix(toeplitz(c(1, -0.1, rep(0, n - 2))))
## Sample the model 100 times (increase for better estimate)
X <- mu.x + solve(chol(Q.x), matrix(rnorm(n = n * 1000), nrow = n, ncol = 1000))
## calculate the positive excursion function
res.x <- excursions.mc(X, alpha = 0.05, type = ">", u = 0)
## Plot the excursion function and the marginal excursion probabilities
plot(res.x$F,
  type = "l",
  main = "Excursion function (black) and marginal probabilites (red)"
)
lines(res.x$rho, col = 2)