User Interface to Multiple Multivariate Normal Distributions

A simple user interface for computing on multiple multivariate normal distributions.

Usage

mvnorm(mean, invcholmean, chol, invchol)
# S3 method for class 'mvnorm'
aperm(a, perm, ...)
margDist(object, which, ...)
# S3 method for class 'mvnorm'
margDist(object, which, ...)
condDist(object, which_given, given, ...)
# S3 method for class 'mvnorm'
condDist(object, which_given, given, ...)
# S3 method for class 'mvnorm'
simulate(object, nsim = dim(object$scale)[1L], seed = NULL, 
                            standardize = FALSE, as.data.frame = FALSE, ...)
# S3 method for class 'mvnorm'
logLik(object, obs, lower, upper, standardize = FALSE, ...)
# S3 method for class 'mvnorm'
lLgrad(object, obs, lower, upper, standardize = FALSE, ...)

Arguments

chol

either an ltMatrices object specifying (multiple) Cholesky factors of the covariance matrix or one single numeric lower triangular square matrix.

invchol

either an ltMatrices object specifying (multiple) inverse Cholesky factors of the covariance matrix or one single numeric lower triangular square matrix.

a,object

objects of class mvnorm.

perm

a permutation of the covariance matrix corresponding to a.

which

names or indices of elements those marginal distribution is of interest.

which_given

names or indices of elements to condition on.

given

matrix of realisations to condition on (number of rows is equal to length(which), the number of columns corresponds to the number of matrices in chol or invchol.

lower

matrix of lower limits (one column for each observation, \(J\) rows).

upper

matrix of upper limits (one column for each observation, \(J\) rows).

obs

matrix of exact observations (one column for each observation, \(J\) rows).

mean

matrix of means (one column for each observation, length is recycled to length of obs, lower and upper).

invcholmean

matrix of scaled means, that is, invchol %*% mean, one column for each observation, length is recycled to length of obs, lower and upper.

seed

an object specifying if and how the random number generator should be initialized, see simulate.

standardize

logical, should the Cholesky factor (or its inverse) undergo standardization (ensuring the covariance matrix is a correlation matrix) before computing the likelihood.

nsim

number of samples to draw.

as.data.frame

logical, convert the $J x N$ matrix result to a classical $N x J$ data frame.

...

Additional arguments to ldpmvnorm and sldpmvnorm

Details

The constructor mvnorm can be used to specify (multiple) multivariate normal distributions. margDist derives marginal and condDist conditional distributions from such objects. A simulate method exists for drawn samples from multivariate normals.

The continuous (data in obs), discrete (intervals in lower and upper), and mixed continuous-discrete log-likelihood is implemented in logLik. The corresponding gradients with respect to all model parameters and with respect to the data arguments is available from lLgrad.

Rationals and examples are given in Chapter 7 of the package vignette linked to below.

Value

mvnorm, margDist, and condDist return objects of class mvnorm. logLik returns the log-likelihood and lLgrad a list with gradients.

See also

vignette("lmvnorm_src", package = "mvtnorm")