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Gibbs Sampler for the truncated multivariate normal distribution

Source: R/The_Gibbs_Sampler.R
rtmvnorm.gibbs.Rd

rtmvnorm.gibbs implements Gibbs sampler for the truncated multivariate normal distribution with covariance matrix covmat.

Usage

rtmvnorm.gibbs(
  n_sim = 1e+05,
  covmat,
  lower = -Inf,
  upper,
  fixed = (lower == upper),
  out = c(1),
  burn_in = 1000
)

Arguments

n_sim

A positive number representing the number of draws from the Gibbs sampler after burn-in.. Defaults to 1e+05.

covmat

A symmetric and numeric matrix representing the covariance matrix for the multivariate normal distribution.

lower

A number or numeric vector representing the lower cutoff point(s) for the truncated normal distribution. The length of lower must be 1 or equal to the dimension of the multivariable normal distribution. Defaults to -Inf.

upper

A number or numeric vector representing the upper cutoff point(s) for the truncated normal distribution. Must be greater or equal to lower. In addition the length of upper must be 1 or equal to the dimension of the multivariable normal distribution. Defaults to Inf.

fixed

A logical scalar or a logical vector indicating which variables to fix. If fixed is a vector, it must have the same length as lower and upper. Defaults to TRUE when lower is equal to upper and FALSE otherwise.

out

An integer or numeric vector indicating which variables should be returned from the Gibbs sampler. If out = c(1), the first variable (usually the genetic component of the full liability of the first phenotype) is estimated and returned. If out = c(2), the second variable (usually full liability) is estimated and returned. If out = c(1,2), both the first and the second variable are estimated and returned. Defaults to c(1).

burn_in

A number of iterations that count as burn in for the Gibbs sampler. Must be non-negative. Defaults to 1000.

Value

If covmat is a symmetric and numeric matrix, if n_sim and burn_in are positive/non-negative numbers, if out is a numeric vector and lower, upper and fixed are numbers or vectors of the same length and the required format, rtmvnorm.gibbs returns the sampling values from the Gibbs sampler for all variables specified in out.

Details

Given a covariance matrix covmat and lower and upper cutoff points, the function rtmvnorm.gibbs() can be used to perform Gibbs sampler on a truncated multivariable normal distribution. It is possible to specify which variables to return from the Gibbs sampler, making it convenient to use when estimating only the full liability or the genetic component of the full liability.

References

Kotecha, J. H., & Djuric, P. M. (1999, March). Gibbs sampling approach for generation of truncated multivariate gaussian random variables. In 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No. 99CH36258) (Vol. 3, pp. 1757-1760). IEEE. doi:10.1109/ICASSP.1999.756335

Wilhelm, S., & Manjunath, B. G. (2010). tmvtnorm: A package for the truncated multivariate normal distribution. The R Journal. doi:10.32614/RJ-2010-005

Examples

samp <- rtmvnorm.gibbs(10e3, covmat = matrix(c(1, 0.2, 0.2, 0.5), 2),
                       lower = c(-Inf, 0), upper = c(0, Inf), out = 1:2)