Simultaneous confidence regions using Monte Carlo samples

simconf.mc is used for calculating simultaneous confidence regions based on Monte Carlo samples. The function returns upper and lower bounds \(a\) and \(b\) such that \(P(a<x<b) = 1-\alpha\).

Usage

simconf.mc(samples, alpha, ind, verbose = FALSE)

Arguments

samples: Matrix with model Monte Carlo samples. Each column contains a sample of the model.
alpha: Error probability for the region.
ind: Indices of the nodes that should be analyzed (optional).
verbose: Set to TRUE for verbose mode (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

See simconf() for details.

Author

David Bolin davidbolin@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))))
## Sample the model 100 times (increase for better estimate)
X <- mu.x + solve(chol(Q.x), matrix(rnorm(n = n * 100), nrow = n, ncol = 100))
## calculate the confidence region
conf <- simconf.mc(X, 0.2)
#> 0.02017992
## 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)