excursions (version 2.5.8)

simconf: Simultaneous confidence regions for Gaussian models

Description

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

Usage

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

Value

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.

Arguments

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).

Author

David Bolin and Finn Lindgren

Details

The pointwise confidence bands are based on the marginal quantiles, meaning that a.marignal is a vector where the ith element equals \(\mu_i + q_{\alpha,i}\) and b.marginal is a vector where the ith element equals \(\mu_i + q_{1-\alpha,i}\), where \(\mu_i\) is the expected value of the \(x_i\) and \(q_{\alpha,i}\) is the \(\alpha\)-quantile of \(x_i-\mu_i\).

The simultaneous confidence band is defined by the lower limit vector a and the upper limit vector b, where \(a_i = \mu_i +c q_{\alpha}\) and \(b_i = \mu_i + c q_{1-\alpha}\), where \(c\) is a constant computed such that \(P(a < x < b) = 1-\alpha\).

References

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.

See Also

simconf.inla, simconf.mc, simconf.mixture

Examples

## 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)