rcmvtruncnorm {condTruncMVN}

Random Sample from Conditional Truncated Multivariate Normal

Description

Randomly samples from conditional truncated multivariate normal distribution variate, Y|X, where Z = (X, Y) is the fully joint multivariate normal distribution with mean, covariance matrix sigma, and truncated between lower and upper. See the vignette for more information.

Usage

rcmvtruncnorm(
  n,
  mean,
  sigma,
  lower,
  upper,
  dependent.ind,
  given.ind,
  X.given,
  init = rep(0, length(mean)),
  burn = 10L,
  thin = 1
)

Arguments

n

number of random samples desired (sample size).

mean

the mean vector for Z of length of n

sigma

the symmetric and positive-definite covariance matrix of dimension n x n of Z.

lower

a vector of lower bounds of length n that truncate Z

upper

a vector of upper bounds of length n that truncate Z

dependent.ind

a vector of integers denoting the indices of dependent variable Y.

given.ind

a vector of integers denoting the indices of conditioning variable X. If specified as integer vector of length zero or left unspecified, the unconditional density is returned.

X.given

a vector of reals denoting the conditioning value of X. This should be of the same length as given.ind

init

initial value used for random generation of truncated multivariate normal in a Gibbs sampler. Default: A vector of zeros, equal to the number of components. For details, see tmvmixnorm::rtmvn().

burn

the burn-in, which is the number of initial iterations to be discarded. Default: 10. Passed to rtmvn().

thin

thinning lag (default as 1).

Note

Uses rtmvn from the tmvmixnorm package to find the random variate.

Examples

# Generate 2 random numbers from X2,X3,X5|X2,X4 ~ N_3(1, Sigma)
# truncated between -10 and 10.
d <- 5
rho <- 0.9
Sigma <- matrix(0, nrow = d, ncol = d)
Sigma <- rho^abs(row(Sigma) - col(Sigma))

set.seed(2342)
rcmvtruncnorm(2,
  mean = rep(1, d),
  sigma = Sigma,
  lower = rep(-10, d),
  upper = rep(10, d),
  dependent.ind = c(2, 3, 5),
  given.ind = c(1, 4), X.given = c(1, -1)
)

# Example 2: Generate two random numbers from
# X1|X2, X3, X4, X5 ~ N(1, Sigma) truncated between -10 and 10.
set.seed(2342)
rcmvtruncnorm(2,
  mean = rep(1, d),
  sigma = Sigma,
  lower = rep(-10, d),
  upper = rep(10, d),
  dependent.ind = 1,
  given.ind = 2:5, X.given = c(1, -1, 1, -1)
)