algorithms {mvtnorm}R Documentation

Choice of Algorithm and Hyper Parameters

Description

Choose between three algorithms for evaluating normal (and t-) distributions and define hyper parameters.

Usage

GenzBretz(maxpts = 25000, abseps = 0.001, releps = 0)
Miwa(steps = 128, checkCorr = TRUE, maxval = 1e3)
TVPACK(abseps = 1e-6)

Arguments

maxpts

maximum number of function values as integer. The internal FORTRAN code always uses a minimum number depending on the dimension. (for example 752 for three-dimensional problems).

abseps

absolute error tolerance; for TVPACK only used for dimension 3.

releps

relative error tolerance as double.

steps

number of grid points to be evaluated; cannot be larger than 4097.

checkCorr

logical indicating if a check for singularity of the correlation matrix should be performed (once per function call to pmvt() or pmvnorm()).

maxval

replacement for Inf when non-orthant probabilities involving Inf shall be computed.

Details

There are three algorithms available for evaluating normal (and two algorithms for t-) probabilities: The default is the randomized Quasi-Monte-Carlo procedure by Genz (1992); Genz (1993) and Genz and Bretz (2002) applicable to arbitrary covariance structures and dimensions up to 1000.

For normal probabilities, smaller dimensions (up to 20) and non-singular covariance matrices, the algorithm by Miwa, Hayter, and Kuriki (2003) can be used as well. This algorithm can compute orthant probabilities (lower being -Inf or upper equal to Inf). Non-orthant probabilities are computed from the corresponding orthant probabilities, however, infinite limits are replaced by maxval along with a warning.

For two- and three-dimensional problems and semi-infinite integration region, TVPACK implements an interface to the methods described by Genz (2004).

Value

An object of class "GenzBretz", "Miwa", or "TVPACK" defining hyper parameters.

References

Genz A (1992). “Numerical Computation of Multivariate Normal Probabilities.” Journal of Computational and Graphical Statistics, 1(2), 141–149. doi:10.1080/10618600.1992.10477010.

Genz A (1993). “Comparison of Methods for the Computation of Multivariate Normal Probabilities.” Computing Science and Statistics, 25, 400–405.

Genz A (2004). “Numerical Computation of Rectangular Bivariate and Trivariate Normal and t Probabilities.” Statistics and Computing, 14(3), 251–260. doi:10.1023/B:STCO.0000035304.20635.31.

Genz A, Bretz F (2002). “Methods for the Computation of Multivariate t Probabilities.” Journal of Computational and Graphical Statistics, 11(4), 950–971. doi:10.1198/106186002394.

Miwa T, Hayter AJ, Kuriki S (2003). “The Evaluation of General Non-centred Orthant Probabilities.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(1), 223–234. doi:10.1111/1467-9868.00382.

[Package mvtnorm version 1.4-2 Index]