rtmvnorm {tmvtnsim}

Random Generation for Truncated Multivariate Normal

Description

Draws from truncated multivariate normal distribution subject to linear inequality constraints represented by a matrix.

Usage

rtmvnorm(
  mean,
  sigma,
  blc = NULL,
  lower,
  upper,
  init = NULL,
  burn = 10,
  n = NULL
)

Arguments

mean

n x p matrix of means. The number of rows is the number of observations. The number of columns is the dimension of the problem.

sigma

p x p covariance matrix.

blc

m x p matrix of coefficients for linear inequality constraints. If NULL, the p x p identity matrix will be used.

lower

n x m or 1 x m matrix of lower bounds for truncation.

upper

n x m or 1 x m matrix of upper bounds for truncation.

init

n x p or 1 x p matrix of initial values. If NULL, default initial values will be generated.

burn

number of burn-in iterations. Defaults to 10.

n

number of random samples when mean is a vector.

Value

Returns an n x p matrix of random numbers following the specified truncated multivariate normal distribution.

Examples

# Example 1: full rank blc
d = 3;
rho = 0.9;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = diag(1,d);
n = 1000;
mean = matrix(rep(1:d,n), nrow=n, ncol=d, byrow=TRUE);
set.seed(1203)
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=50)
apply(result, 2, summary)

# Example 2: use the alternative form of input
set.seed(1203)
result = rtmvnorm(mean=1:d, sigma, blc, -1, 1, burn=50, n=1000)
apply(result, 2, summary)

# Example 3: non-full rank blc
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = matrix(c(1,1,1,0,1,0,1,0,1), ncol=d);
n = 100;
mean = matrix(rep(1:d,n), nrow=n, ncol=d, byrow=TRUE);
set.seed(1228)
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=10)
apply(result, 2, summary)

# Example 4: non-full rank blc, alternative form of input
set.seed(1228)
result = rtmvnorm(mean=1:d, sigma, blc, -1, 1, burn=10, n=100)
apply(result, 2, summary) 

# Example 5: means, lower, or upper bounds differ across samples
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = matrix(c(1,0,1,1,1,0), ncol=d, byrow=TRUE)
n = 100;
set.seed(3084)
mean = matrix(runif(n*d), nrow=n, ncol=d);
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=50)
apply(result, 2, summary)