zigzagHMC: Sample from a truncated Gaussian distribution
In hdtg: Generate Samples from Multivariate Truncated Normal Distributions

zigzagHMC

R Documentation

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
)

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.

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

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.

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))

hdtg documentation built on Jan. 26, 2026, 9:06 a.m.