excursions (version 2.0.6)

gaussint: Sequential estimation of Gaussian integrals

Description

gaussint is used for calculating Gaussian integrals $$latex$$ A limit value $lim$ can be used to stop the integration if the sequential estimate goes below the limit, which can result in substantial computational savings in cases when one only is interested in testing if the integral is above the limit value. The integral is calculated sequentially, and estimates for all subintegrals are also returned.

Usage

gaussint(mu,
         Q.chol,
         Q,
         a,
         b,
         lim = 0,
         n.iter = 10000,
         ind,
         use.reordering = c("natural","sparsity","limits"),
         max.size,
         max.threads=0,
         seed,
         LDL=FALSE)

Arguments

mu

Expectation vector for the Gaussian distribution.

Q.chol

The Cholesky factor of the precision matrix (optional)

Q

Precision matrix for the Gaussian distribution. If Q is supplied but not Q.chol, the cholesky factor is computed before integrating.

a

Lower limit in integral.

b

Upper limit in integral.

lim

If this argument is used, the integration is stopped and 0 is returned if the estimated value goes below $lim$.

n.iter

Number or iterations in the MC sampler that is used for approximating probabilities. The default value is 10000.

ind

Indices of the nodes that should be analyzed (optional)

use.reordering

Determines what reordering to use:

• "natural"

{No reordering is performed.} "sparsity"{Reorder for sparsity in the cholesky factor (MMD reordering is used).} "limits"{Reorder by moving all nodes wi

Value

• A list:
• P
  Value of the integral.
• E
  Estimated error of the P estimate.
• Pv
  A vector with the estimates of all sub-integrals.
• Ev
  A vector with the estimated errors of the Pv estimates

item

• max.size
• max.threads
• seed
• LDL

References

Bolin, D. and Lindgren, F. (2013) Excursion and contour uncertainty regions for latent Gaussian models, Journal of the Royal Statistical Society: Series B (in press).

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 probability that the process is between mu-3 and mu+3
prob = gaussint(mu=mu.x, Q=Q.x, a= mu.x-3, b=mu.x+3, max.threads=2)
prob$P