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