Simultaneous confidence regions for Gaussian mixture models

simconf.mixture is used for calculating simultaneous confidence regions for Gaussian mixture models. The distribution for the process $x$ is assumed to be $$\pi(x) = \sum_{k=1}^K w_k N(\mu_k, Q_k^{-1}).$$ The function returns upper and lower bounds $a$ and $b$ such that $P(a<x<b) = 1-\alpha$.

Usage

simconf.mixture(
  alpha,
  mu,
  Q,
  w,
  ind,
  n.iter = 10000,
  vars,
  verbose = FALSE,
  max.threads = 0,
  seed = NULL,
  mix.samp = TRUE,
  tol = NULL
)

Arguments

alpha: Error probability for the region.
mu: A list with the k expectation vectors $\mu_k$.
Q: A list with the k precision matrices $Q_k$.
w: A vector with the weights for each class in the mixture.
ind: Indices of the nodes that should be analyzed (optional).
n.iter: Number or iterations in the MC sampler that is used for approximating probabilities. The default value is 10000. If tol is given, this is the maximal number of iterations.
vars: A list with precomputed marginal variances for each class (optional).
verbose: Set to TRUE for verbose mode (optional).
max.threads: The number of threads that the program can use. The default, 0, uses the default number of threads of OpenMP, which can be set with the environment variable OMP_NUM_THREADS. The number of threads is at most OMP_THREAD_LIMIT, and is one if the package was built without OpenMP.
seed: Random seed (optional).
mix.samp: If TRUE, the MC integration is done by directly sampling the mixture, otherwise sequential integration is used.
tol: Target for the estimated errors of the probabilities that are computed to find the band (optional), see simconf(). It is only used if mix.samp = FALSE.

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.
mean: The mean of the mixture.
vars: The marginal variances of the mixture.

Details

See simconf() for details.

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

Examples

n <- 11
K <- 3
mu <- Q <- list()
for (k in 1:K) {
  mu[[k]] <- k * 0.1 + seq(-5, 5, length = n)
  Q[[k]] <- Matrix(toeplitz(c(1, -0.1, rep(0, n - 2))))
}
## calculate the confidence region
conf <- simconf.mixture(0.05, mu, Q, w = rep(1 / 3, 3), max.threads = 2)

## Plot the region
plot(mu[[1]], type = "l")
lines(mu[[2]])
lines(mu[[3]])
lines(conf$a, col = 2)
lines(conf$b, col = 2)