mh: Upper Cholesky factor sampling using Metropolis-Hastings
In gmat: Simulation of Graphical Correlation Matrices

Description Usage Arguments Details Author(s) References Examples

Metropolis-Hasting algorithms to sample the upper Cholesky factor, using positive hemispheres of different dimensions. A zero pattern may be specified using an acyclic digraph.

1
2
3

mh_u(N = 1, p = 3, dag = NULL, ...)

mh_sphere(N = 1, k, i = 1, h = 100, eps = 0.01)

`N`	Number of samples.
`p`	Dimension of the upper Cholesky factor.
`dag`	An igraph acyclic digraph specifying the zero pattern in the upper Cholesky factor of the sampled matrices. Nodes must be in ancestral order, with the first one having no parents.
`...`	Additional parameters for `mh_sphere()`.
`k`	Dimension of the hemisphere from which the sample is taken.
`i`	Integer, power of the first coordinate in the density.
`h`	Heating phase size.
`eps`	Perturbation variance.

Function mh_u() returns a sample of N upper Cholesky factors whose rows have been generated using mh_sphere(). The dimensions of the hemispheres used to sample vary depending both on the row number of the Cholesky factor, and whether there is a zero pattern specified by dag.

The details of the algorithm implemented by mh_sphere() can be found in the paper Córdoba et al. (2018), including a discussion on theoretical convergence and numerical experiments for choosing its hyper parameters h and eps.

Gherardo Varando gherardo.varando@math.ku.dk

Córdoba I., Varando G., Bielza C., Larrañaga P. A fast Metropolis-Hastings method for generating random correlation matrices. Lecture Notes in Computer Science (IDEAL 2018), vol 11314, pp. 117-124, 2018.

## Upper Cholesky factor sampling
# Generate a random acyclic digraph
dag <- rgraph(p = 3, d = 0.5, dag = TRUE)
igraph::print.igraph(dag)

# Generate an upper Cholesky factor complying with such zero pattern
mh_u(dag = dag)
# We may also generate it with no zero pattern (full upper triangular)
mh_u()
## Hemisphere sampling
# 3D hemisphere from a density proportional to the square of the first coordinate
mh_sphere(N = 4, k = 3, i = 2)