.cholpermGB {TruncatedNormal} | R Documentation |
Cholesky matrix decomposition with GGE ordering
Description
This function computes the Cholesky decomposition of a covariance matrix
Sigma
and returns a list containing the permuted bounds for integration.
The prioritization of the variables follow the rule proposed in Gibson, Glasbey and Elston (1994)
and reorder variables to have outermost variables with smallest expected values.
Usage
.cholpermGB(Sigma, l, u)
Arguments
Sigma |
|
l |
|
u |
|
Details
The list contains an integer vector perm
with the indices of the permutation, which is such that
Sigma(perm, perm) == L %*% t(L)
.
The permutation scheme is described in Genz and Bretz (2009) in Section 4.1.3, p.37.
Value
a list with components
L
: Cholesky rootl
: permuted vector of lower boundsu
: permuted vector of upper boundsperm
: vector of integers with ordering of permutation
References
Genz, A. and Bretz, F. (2009). Computations of Multivariate Normal and t Probabilities, volume 105. Springer, Dordrecht.
Gibson G.J., Glasbey C.A. and D.A. Elton (1994). Monte Carlo evaluation of multivariate normal integrals and sensitivity to variate ordering. In: Dimon et al., Advances in Numerical Methods and Applications, WSP, pp. 120-126.