rmvnorm_max_chol: Maximal coupling of two multivariate Normal distributions

In pierrejacob/debiasedmcmc: Unbiased MCMC with couplings

Maximal coupling of two multivariate Normal distributions

Description

Sample from maximal coupling of two multivariate Normal distributions, specified through their means, the Cholesky factors of their covariance matrices, and the inverse of the Cholesky factors of the covariance matrices.

Usage

rmvnorm_max_chol(
  mu1,
  mu2,
  Cholesky1,
  Cholesky2,
  Cholesky_inverse1,
  Cholesky_inverse2
)

Arguments

mu1	First mean
mu2	First mean
Cholesky1	First Cholesky factor, e.g. obtained with chol
Cholesky2	Second Cholesky factor
Cholesky_inverse1	First inverse of Cholesky factor, e.g. obtained with solve(chol(Sigma))
Cholesky_inverse2	Second inverse of Cholesky factor

Value

A list containing 'xy', a matrix with 2 columns (one for each draw), and a boolean indicator 'identical' indicating whether the two draws are identical.

Examples

p <- 3
mu1 <- rep(0, p)
mu2 <- rep(1, p)
Sigma1 <- diag(0.4, p, p)
Sigma1[1,2] <- Sigma1[2,1] <- 0.2
Sigma2 <- diag(1.4, p, p)
Sigma2[1,2] <- Sigma2[2,1] <- -0.5
Sigma1_chol <- chol(Sigma1)
Sigma2_chol <- chol(Sigma2)
Sigma1_chol_inv <- solve(Sigma1_chol)
Sigma2_chol_inv <- solve(Sigma2_chol)
rmvnorm_max_chol(mu1, mu2, Sigma1_chol, Sigma2_chol, Sigma1_chol_inv, Sigma2_chol_inv)

pierrejacob/debiasedmcmc documentation built on Aug. 22, 2022, 12:41 a.m.