mvtnorm (version 1.3-3)

lpRR: Multivariate Normal Log-likelihood and Score Functions for Reduced Rank Covariances

Description

Computes the log-likelihood (contributions) of interval-censored observations from multivariate normal distributions with reduced rank structure and evaluates corresponding score functions.

Usage

lpRR(lower, upper, mean = 0, B, D = rep(1, nrow(B)), 
     Z, weights = 1 / ncol(Z), log.p = TRUE)
slpRR(lower, upper, mean = 0, B, D = rep(1, nrow(B)), 
      Z, weights = 1 / ncol(Z), log.p = TRUE)

Value

The log-likelihood (log.p = TRUE) or corresponding probability. slpRR return the scores.

Arguments

lower

vector of lower limits (one element for each dimension, \(J\) elements).

upper

vector of upper limits (one element for each dimension, \(J\) elements).

mean

vector of means (one element for each dimension, length is recycled to length of lower and upper).

B

matrix of dimension \(J \times K\).

D

vector of \(J\) diagonal elements.

Z

matrix of standard normal random variables, with \(K\) nrows.

weights

optional weights.

log.p

logical. By default, log-probabilities are returned.

Details

Evaluates the multivariate normal log-likelihood defined by means, B and D when the covariance is \(Sigma = B B^\top + D\) over boxes defined by lower and upper. Details are given in Genz and Bretz (2009, Chapter 2.3.1.).

slpmvnorm computes the corresponding score functions with respect to lower, upper, mean, B and D.

More details can be found in the lmvnorm_src package vignette.

References

Genz, A. and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195. Springer-Verlag, Heidelberg.

See Also

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

Examples

  J <- 6
  K <- 3
  B <- matrix(rnorm(J * K), nrow = J)
  D <- runif(J)
  S <- tcrossprod(B) + diag(D)
  a <- -(2 + runif(J))
  b <- 2 + runif(J)
  M <- 1e4
  Z <- matrix(rnorm(K * M), nrow = K)
  lpRR(lower = a, upper = b, B = B, D = D, Z = Z)