randmvn: Randomly Generate a Multivariate Normal Distribution

In monomvn: Estimation for MVN and Student-t Data with Monotone Missingness

Randomly Generate a Multivariate Normal Distribution

Description

Randomly generate a mean vector and covariance matrix describing a multivariate normal (MVN) distribution, and then sample from it

Usage

randmvn(N, d, method = c("normwish", "parsimonious"),
        mup=list(mu = 0, s2 = 1), s2p=list(a = 0.5, b = 1),
        pnz=0.1, nu=Inf)

Arguments

N	number of samples to draw
d	dimension of the MVN, i.e., the length of the mean vector and the number of rows/cols of the covariance matrix
method	the default generation method is "norwish" uses the direct method described in the details section below, whereas the "parsimonious" method builds up the random mean vector and covariance via regression coefficients, intercepts, and variances. See below for more details. Here, a random number of regression coefficients for each regression are set to zero
mup	a list with entries $mu and $s2: $mu is the prior mean for the independent components of the normally distributed mean vector; $s2 is the prior variance
s2p	a list with entries $a and $b only valid for method = "parsimonious": $a > 0 is the baseline inverse gamma prior scale parameter for the regression variances (the actual parameter used for each column i in 1:d of the covariance matrix is a + i - 1); $b >= 0 is the rate parameter
pnz	a scalar 0 <= pnz <= 1, only valid for method = "parsimonious": determines the binomial proportion of non-zero regression coefficients in the sequential build-up of mu and S, thereby indirectly determining the number of non-zero entries in S
nu	a scalar >= 1 indicating the degrees of freedom of a Student-t distribution to be used instead of an MVN when not infinite

Details

In the direct method ("normwish") the components of the mean vector mu are iid from a standard normal distribution, and the covariance matrix S is drawn from an inverse–Wishart distribution with degrees of freedom d + 2 and mean (centering matrix) diag(d)

In the "parsimonious" method mu and S are built up sequentially by randomly sampling intercepts, regression coefficients (of length i-1 for i in 1:d) and variances by applying the monomvn equations. A unique prior results when a random number of the regression coefficients are set to zero. When none are set to zero the direct method results

Value

The return value is a list with the following components:

mu	randomly generated mean vector of length d
S	randomly generated covariance matrix with d rows and d columns
x	if N > 0 then x is an N*d matrix of N samples from the MVN with mean vector mu and covariance matrix S; otherwise when N = 0 this component is not included

Note

requires the rmvnorm function of the mvtnorm package

Author(s)

Robert B. Gramacy [e-mail]

See Also

rwish, rmvnorm, rmono

Examples

randmvn(5, 3)

monomvn documentation built on Sept. 30, 2024, 9:45 a.m.