hdtg (version 0.3.3)

zigzagHMC: Sample from a truncated Gaussian distribution

Description

Generate MCMC samples from a d-dimensional truncated Gaussian distribution with element-wise truncations using the Zigzag Hamiltonian Monte Carlo sampler (Zigzag-HMC).

Usage

zigzagHMC(
  nSample,
  burnin = 0,
  mean,
  prec,
  lowerBounds,
  upperBounds,
  init = NULL,
  stepSize = NULL,
  nutsFlg = FALSE,
  precondition = FALSE,
  seed = 1,
  numThreads = 1,
  diagnosticMode = FALSE
)

Value

When diagnosticMode = FALSE (default), returns an nSample-by-d matrix of samples.

When diagnosticMode = TRUE, returns a list with elements:

samples

nSample-by-d matrix of samples

stepsize

The step size used for sampling

Arguments

nSample

number of samples after burn-in.

burnin

number of burn-in samples (default = 0).

mean

a d-dimensional mean vector.

prec

a d-by-d precision matrix of the Gaussian distribution.

lowerBounds

a d-dimensional vector specifying the lower bounds. -Inf is accepted.

upperBounds

a d-dimensional vector specifying the upper bounds. Inf is accepted.

init

a d-dimensional vector of the initial value. init must satisfy all constraints. If init = NULL, a random initial value will be used.

stepSize

step size for Zigzag-HMC or Zigzag-NUTS (if nutsFlg = TRUE). Default value is the empirically optimal choice: sqrt(2)(lambda)^(-1/2) for Zigzag-HMC and 0.1(lambda)^(-1/2) for Zigzag-NUTS, where lambda is the minimal eigenvalue of the precision matrix.

nutsFlg

logical. If TRUE the No-U-Turn sampler will be used (Zigzag-NUTS).

precondition

logical. If TRUE, the precision matrix will be preconditioned so that its diagonals (i.e. conditional variances) are all 1.

seed

random seed (default = 1).

numThreads

number of threads for parallel execution (default = 1). Set to 0 for automatic detection of available cores.

diagnosticMode

logical. TRUE for also returning diagnostic information such as the stepsize used.

References

Nishimura, A., Zhang, Z., and Suchard, M. A. (2024). Zigzag path connects two Monte Carlo samplers: Hamiltonian counterpart to a piecewise deterministic Markov process. Journal of the American Statistical Association, 1-13.

Nishimura, A., Dunson, D. B., and Lu, J. (2020). Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods. Biometrika, 107(2): 365-380.

See Also

getZigzagSample(), createEngine(), createNutsEngine(), setMean(), setPrecision()

Examples

set.seed(1)
d <- 10
A <- matrix(runif(d^2)*2-1, ncol=d)
precMat <- t(A) %*% A
initial <- rep(1, d)
results <- zigzagHMC(nSample = 1000, burnin = 1000, mean = rep(0, d), prec = precMat,
lowerBounds = rep(0, d), upperBounds = rep(Inf, d))