excursions (version 2.0.6)

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

Usage

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

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)

LDL

Use LDL factorisations? This is useful for analysis of problems with positive semidefinite precisions.

Value

• A list:
• 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.

References

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

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)