simconf: Simultaneous confidence regions for Gaussian models
In finnlindgren/excursions: Excursion Sets and Contour Credibility Regions for Random Fields

Description Usage Arguments Details Value Author(s) References See Also Examples

simconf is used for calculating simultaneous confidence regions for Gaussian models x. The function returns upper and lower bounds a and b such that P(a<x<b) = 1-alpha.

simconf(
  alpha,
  mu,
  Q,
  n.iter = 10000,
  Q.chol,
  vars,
  ind = NULL,
  verbose = 0,
  max.threads = 0,
  seed = NULL
)

`alpha`	Error probability for the region.
`mu`	Expectation vector for the Gaussian distribution.
`Q`	Precision matrix for the Gaussian distribution.
`n.iter`	Number or iterations in the MC sampler that is used for approximating probabilities. The default value is 10000.
`Q.chol`	The Cholesky factor of the precision matrix (optional).
`vars`	Precomputed marginal variances (optional).
`ind`	Indices of the nodes that should be analyzed (optional).
`verbose`	Set to TRUE for verbose mode (optional).
`max.threads`	Decides the number of threads the program can use. Set to 0 for using the maximum number of threads allowed by the system (default).
`seed`	Random seed (optional).

The pointwise confidence bands are based on the marginal quantiles, meaning that a.marignal = mu + q_{alpha} and b.marginal = mu + q_{1-alpha}, where mu is the mean and q_{alpha} is a vector with the alpha-quantiles of x-mu.

The simultaneous confidence bands are defined as a = mu + c*q_{alpha} and b = mu + c*q_{1-alpha}, where c is a constant computed such that P(a < x < b) = 1-alpha.

An object of class "excurobj" with elements

`a`	The lower bound.
`b`	The upper bound.
`a.marginal`	The lower bound for pointwise confidence bands.
`b.marginal`	The upper bound for pointwise confidence bands.

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

Bolin et al. (2015) Statistical prediction of global sea level from global temperature, Statistica Sinica, vol 25, pp 351-367.

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.

simconf.inla, simconf.mc, simconf.mixture

## Create mean and a tridiagonal precision matrix
n = 11
mu.x = seq(-5, 5, length=n)
Q.x = Matrix(toeplitz(c(1, -0.1, rep(0, n-2))))
## calculate the confidence region
conf = simconf(0.05, mu.x, Q.x, max.threads=2)
## Plot the region
plot(mu.x, type="l", ylim=c(-10, 10),
     main='Mean (black) and confidence region (red)')
lines(conf$a, col=2)
lines(conf$b, col=2)