Package 'hdtg' reference manual

Title:	Generate Samples from Multivariate Truncated Normal Distributions
Description:	Efficient sampling from high-dimensional truncated Gaussian distributions, or multivariate truncated normal (MTN). Techniques include zigzag Hamiltonian Monte Carlo as in Akihiko Nishimura, Zhenyu Zhang and Marc A. Suchard (2024) <doi:10.1080/01621459.2024.2395587>, and harmonic Monte Carlo in Ari Pakman and Liam Paninski (2014) <doi:10.1080/10618600.2013.788448>.
Authors:	Zhenyu Zhang [aut, cre], Andrew Chin [aut], Akihiko Nishimura [aut], Marc A. Suchard [aut], John W. Ratcliff et al. [cph, ctb] (authors and copyright holders of see2neon.h under an MIT license)
Maintainer:	Zhenyu Zhang <[email protected]>
License:	MIT + file LICENSE
Version:	0.3.4
Built:	2026-05-12 09:31:21 UTC
Source:	https://github.com/cran/hdtg

Efficient Cholesky decomposition

Description

Compute Cholesky decomposition of a matrix.

Usage

cholesky(A)
cholesky(A)

Arguments

A

matrix to decompose

Value

upper triangular matrix R such that A = U'U.

Examples

# Larger example
set.seed(123)
B <- matrix(rnorm(16), 4, 4)
B <- t(B) %*% B  # Make symmetric positive definite
U <- cholesky(B)
U
# Verify decomposition
all.equal(B, t(U) %*% U)
# Larger example
set.seed(123)
B <- matrix(rnorm(16), 4, 4)
B <- t(B) %*% B  # Make symmetric positive definite
U <- cholesky(B)
U
# Verify decomposition
all.equal(B, t(U) %*% U)

Create a Zigzag-HMC engine object

Description

Create the C++ object to set up SIMD vectorization for speeding up calculations for Zigzag-HMC ("Zigzag-HMC engine").

Usage

createEngine(
  dimension,
  lowerBounds,
  upperBounds,
  seed,
  mean,
  precision,
  flags = 128L
)
createEngine(
  dimension,
  lowerBounds,
  upperBounds,
  seed,
  mean,
  precision,
  flags = 128L
)

Arguments

dimension

the dimension of MTN.

lowerBounds

a vector specifying the lower bounds.

upperBounds

a vector specifying the upper bounds.

seed

random seed.

mean

the mean vector.

precision

the precision matrix.

flags

which SIMD instruction set to use. 128 = SSE, 256 = AVX.

Value

a list whose only element is the Zigzag-HMC engine object.

Examples

# Create a 2D engine with simple bounds
dimension <- 2
lowerBounds <- c(-1, -1)
upperBounds <- c(1, 1)
mean <- c(0, 0)
precision <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)
engine <- createEngine(dimension, lowerBounds, upperBounds, 
                       seed = 123, mean, precision, flags = 128)
# Check the engine structure
str(engine)
# Create a 2D engine with simple bounds
dimension <- 2
lowerBounds <- c(-1, -1)
upperBounds <- c(1, 1)
mean <- c(0, 0)
precision <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)
engine <- createEngine(dimension, lowerBounds, upperBounds, 
                       seed = 123, mean, precision, flags = 128)
# Check the engine structure
str(engine)

Create a Zigzag-NUTS engine object

Description

Create the C++ object to set up SIMD vectorization for speeding up calculations for Zigzag-NUTS ("Zigzag-NUTS engine").

Usage

createNutsEngine(
  dimension,
  lowerBounds,
  upperBounds,
  seed,
  stepSize,
  mean,
  precision,
  flags = 128L
)
createNutsEngine(
  dimension,
  lowerBounds,
  upperBounds,
  seed,
  stepSize,
  mean,
  precision,
  flags = 128L
)

Arguments

dimension

the dimension of MTN.

lowerBounds

a vector specifying the lower bounds.

upperBounds

a vector specifying the upper bounds.

seed

random seed.

stepSize

the base step size for Zigzag-NUTS.

mean

the mean vector.

precision

the precision matrix.

flags

which SIMD instruction set to use. 128 = SSE, 256 = AVX.

Value

a list whose only element is the Zigzag-NUTS engine object.

Examples

# Create a Zigzag-NUTS engine for a 2D problem
dimension <- 2
lowerBounds <- c(-2, -2)
upperBounds <- c(2, 2)
stepSize <- 0.1
mean <- c(0.5, -0.5)
precision <- matrix(c(2, 0.3, 0.3, 2), nrow = 2)
nuts_engine <- createNutsEngine(dimension, lowerBounds, upperBounds,
                                seed = 456, stepSize, mean, precision)
str(nuts_engine)
# Create a Zigzag-NUTS engine for a 2D problem
dimension <- 2
lowerBounds <- c(-2, -2)
upperBounds <- c(2, 2)
stepSize <- 0.1
mean <- c(0.5, -0.5)
precision <- matrix(c(2, 0.3, 0.3, 2), nrow = 2)
nuts_engine <- createNutsEngine(dimension, lowerBounds, upperBounds,
                                seed = 456, stepSize, mean, precision)
str(nuts_engine)

Draw a random Laplace momentum

Description

Generate a d-dimensional momentum where the density of each element is proportional to exp(-|pi|).

Usage

drawLaplaceMomentum(d)
drawLaplaceMomentum(d)

Arguments

d

dimension of the momentum.

Value

a d-dimensional Laplace-distributed momentum.

Examples

# Draw a 3-dimensional Laplace momentum with reproducible results
set.seed(3)
momentum <- drawLaplaceMomentum(3)
momentum
# Draw a 3-dimensional Laplace momentum with reproducible results
set.seed(3)
momentum <- drawLaplaceMomentum(3)
momentum

One-step Harmonic HMC Sampler (Whitened Coordinates)

Description

One-step Harmonic HMC Sampler (Whitened Coordinates)

Usage

getHarmonicSample(
  whitenedPosition,
  whitenedConstraints,
  integrationTime,
  diagnosticMode = FALSE,
  seed = NULL
)
getHarmonicSample(
  whitenedPosition,
  whitenedConstraints,
  integrationTime,
  diagnosticMode = FALSE,
  seed = NULL
)

Arguments

whitenedPosition

Position in whitened coordinates

whitenedConstraints

List from applyWhitenTransform()

integrationTime

Time for dynamics simulation

diagnosticMode

Return bounce diagnostics

seed

random seed

Examples

# Basic usage with whitened coordinates
set.seed(123)
whitened_pos <- c(0.1, -0.2, 0.3)
# Create example whitened constraints
whitened_constraints <- list(
  direc = matrix(c(1, 0, 0, 0, 1, 0), nrow = 2, byrow = TRUE),
  direcRowNormSq = c(1, 1),
  bound = c(-0.5, -0.5)
)
result <- getHarmonicSample(
  whitenedPosition = whitened_pos,
  whitenedConstraints = whitened_constraints,
  integrationTime = pi/4
)
result

# With diagnostics enabled
result_diag <- getHarmonicSample(
  whitenedPosition = whitened_pos,
  whitenedConstraints = whitened_constraints,
  integrationTime = pi/4,
  diagnosticMode = TRUE
)
str(result_diag)
# Basic usage with whitened coordinates
set.seed(123)
whitened_pos <- c(0.1, -0.2, 0.3)
# Create example whitened constraints
whitened_constraints <- list(
  direc = matrix(c(1, 0, 0, 0, 1, 0), nrow = 2, byrow = TRUE),
  direcRowNormSq = c(1, 1),
  bound = c(-0.5, -0.5)
)
result <- getHarmonicSample(
  whitenedPosition = whitened_pos,
  whitenedConstraints = whitened_constraints,
  integrationTime = pi/4
)
result

# With diagnostics enabled
result_diag <- getHarmonicSample(
  whitenedPosition = whitened_pos,
  whitenedConstraints = whitened_constraints,
  integrationTime = pi/4,
  diagnosticMode = TRUE
)
str(result_diag)

Get an eligible initial value for a MTN with given mean and truncations

Description

For a given MTN the function returns an initial vector whose elements are one of: (1) middle point of the truncation interval if both lower and upper bounds are finite (2) lower (upper) bound +0.1 (-0.1) if only the lower (upper) bound is finite (3) the corresponding mean value if lower bound = -Inf are upper bound = Inf.

Usage

getInitialPosition(mean, lowerBounds, upperBounds)
getInitialPosition(mean, lowerBounds, upperBounds)

Arguments

mean

a d-dimensional mean vector.

lowerBounds

a d-dimensional vector specifying the lower bounds.

upperBounds

a d-dimensional vector specifying the upper bounds.

Value

an eligible d-dimensional initial vector.

Examples

# Example 1: Bounded interval
mean <- c(0, 0)
lower <- c(-1, -2)
upper <- c(1, 2)
getInitialPosition(mean, lower, upper)

# Example 2: Mixed bounds (some finite, some infinite)
mean <- c(0, 0, 0)
lower <- c(-Inf, 0, -1)
upper <- c(Inf, 5, Inf)
getInitialPosition(mean, lower, upper)

# Example 3: All unbounded (returns mean)
mean <- c(1, 2, 3)
lower <- c(-Inf, -Inf, -Inf)
upper <- c(Inf, Inf, Inf)
getInitialPosition(mean, lower, upper)
# Example 1: Bounded interval
mean <- c(0, 0)
lower <- c(-1, -2)
upper <- c(1, 2)
getInitialPosition(mean, lower, upper)

# Example 2: Mixed bounds (some finite, some infinite)
mean <- c(0, 0, 0)
lower <- c(-Inf, 0, -1)
upper <- c(Inf, 5, Inf)
getInitialPosition(mean, lower, upper)

# Example 3: All unbounded (returns mean)
mean <- c(1, 2, 3)
lower <- c(-Inf, -Inf, -Inf)
upper <- c(Inf, Inf, Inf)
getInitialPosition(mean, lower, upper)

Draw one Markovian zigzag sample

Description

Simulate the Markovian zigzag dynamics for a given position over a specified travel time.

Usage

getMarkovianZigzagSample(position, velocity = NULL, engine, travelTime)
getMarkovianZigzagSample(position, velocity = NULL, engine, travelTime)

Arguments

position

a d-dimensional position vector.

velocity

optional d-dimensional velocity vector. If NULL, it will be generated within the function.

engine

an object representing the Markovian zigzag engine, typically containing settings and state required for the simulation.

travelTime

the duration for which the dynamics are simulated.

Value

A list containing the position and velocity after simulating the dynamics.

Examples

# First create an engine
set.seed(123)
engine <- createEngine(
  dimension = 2,
  lowerBounds = c(-1, -1),
  upperBounds = c(1, 1),
  seed = 123,
  mean = c(0, 0),
  precision = diag(2)
)

# Draw a single Markovian zigzag sample
position <- c(0.1, -0.2)
travel_time <- 0.5
sample_result <- getMarkovianZigzagSample(
  position = position,
  engine = engine,
  travelTime = travel_time
)
sample_result
# First create an engine
set.seed(123)
engine <- createEngine(
  dimension = 2,
  lowerBounds = c(-1, -1),
  upperBounds = c(1, 1),
  seed = 123,
  mean = c(0, 0),
  precision = diag(2)
)

# Draw a single Markovian zigzag sample
position <- c(0.1, -0.2)
travel_time <- 0.5
sample_result <- getMarkovianZigzagSample(
  position = position,
  engine = engine,
  travelTime = travel_time
)
sample_result

Draw one MTN sample with Zigzag-HMC or Zigzag-NUTS

Description

Simulate the Zigzag-HMC or Zigzag-NUTS dynamics on a given MTN.

Usage

getZigzagSample(position, momentum = NULL, nutsFlg, engine, stepSize = NULL)
getZigzagSample(position, momentum = NULL, nutsFlg, engine, stepSize = NULL)

Arguments

position

a d-dimensional initial position vector.

momentum

a d-dimensional initial momentum vector.

nutsFlg

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

engine

list. Its engine element is a pointer to the Zigzag-HMC engine (or Zigzag-NUTS engine) C++ object that implements fast computations for Zigzag-HMC (or Zigzag-NUTS).

stepSize

step size for Zigzag-HMC. If nutsFlg = TRUE, engine contains the base step size for Zigzag-NUTS).

Value

one MCMC sample from the target MTN.

Note

getZigzagSample is particularly efficient when the target MTN has a random mean and covariance/precision where one can reuse the Zigzag-HMC engine object while updating the mean and covariance. The following example demonstrates such a use.

Examples

set.seed(1)
n <- 1000
d <- 10
samples <- array(0, c(n, d))

# initialize MTN mean and precision
m <- rnorm(d, 0, 1)
prec <- rWishart(n = 1, df = d, Sigma = diag(d))[, , 1]
# call createEngine once
engine <- createEngine(dimension = d, lowerBounds = rep(0, d),
 upperBounds = rep(Inf, d), seed = 1, mean = m, precision = prec)

HZZtime <- sqrt(2) / sqrt(min(mgcv::slanczos(
 A = prec, k = 1,
 kl = 1
)[['values']]))

currentSample <- rep(0.1, d)
for (i in 1:n) {
  m <- rnorm(d, 0, 1)
  prec <- rWishart(n = 1, df = d, Sigma = diag(d))[,,1]
  setMean(engine = engine, mean = m)
  setPrecision(engine = engine, precision = prec)
  currentSample <- getZigzagSample(position = currentSample,
                                   nutsFlg = FALSE,
                                   engine = engine,
                                   stepSize = HZZtime)
  samples[i,] <- currentSample
}
set.seed(1)
n <- 1000
d <- 10
samples <- array(0, c(n, d))

# initialize MTN mean and precision
m <- rnorm(d, 0, 1)
prec <- rWishart(n = 1, df = d, Sigma = diag(d))[, , 1]
# call createEngine once
engine <- createEngine(dimension = d, lowerBounds = rep(0, d),
 upperBounds = rep(Inf, d), seed = 1, mean = m, precision = prec)

HZZtime <- sqrt(2) / sqrt(min(mgcv::slanczos(
 A = prec, k = 1,
 kl = 1
)[['values']]))

currentSample <- rep(0.1, d)
for (i in 1:n) {
  m <- rnorm(d, 0, 1)
  prec <- rWishart(n = 1, df = d, Sigma = diag(d))[,,1]
  setMean(engine = engine, mean = m)
  setPrecision(engine = engine, precision = prec)
  currentSample <- getZigzagSample(position = currentSample,
                                   nutsFlg = FALSE,
                                   engine = engine,
                                   stepSize = HZZtime)
  samples[i,] <- currentSample
}

Sample from a truncated Gaussian distribution with the harmonic HMC

Description

Generate MCMC samples from a d-dimensional truncated Gaussian distribution with constraints Fx+g >= 0 using the Harmonic Hamiltonian Monte Carlo sampler (Harmonic-HMC).

Usage

harmonicHMC(
  nSample,
  burnin = 0,
  mean,
  choleskyFactor,
  constrainDirec,
  constrainBound,
  init,
  time = c(pi/8, pi/2),
  precFlg,
  seed = 1,
  extraOutputs = c()
)
harmonicHMC(
  nSample,
  burnin = 0,
  mean,
  choleskyFactor,
  constrainDirec,
  constrainBound,
  init,
  time = c(pi/8, pi/2),
  precFlg,
  seed = 1,
  extraOutputs = c()
)

Arguments

nSample

number of samples after burn-in.

burnin

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

mean

a d-dimensional mean vector.

choleskyFactor

upper triangular matrix R from Cholesky decomposition of precision or covariance matrix into R^TR.

constrainDirec

the k-by-d F matrix (k is the number of linear constraints).

constrainBound

the k-dimensional g vector.

init

a d-dimensional vector of the initial value. init must satisfy all constraints.

time

HMC integration time for each iteration. Can either be a scalar value for a fixed time across all samples, or a length 2 vector of a lower and upper bound for uniform distribution from which the time is drawn from for each iteration.

precFlg

logical. whether choleskyFactor is from precision (TRUE) or covariance matrix (FALSE).

seed

random seed (default = 1).

extraOutputs

vector of strings. "numBounces" and/or "bounceDistances" can be requested, with the latter containing the distances in-between bounces for each sample and hence incurring significant computational and memory costs.

Value

When extraOutputs is empty (default), returns an nSample-by-d matrix of samples.

When extraOutputs contains "numBounces" and/or "bounceDistances", returns a list with elements:

samples

nSample-by-d matrix of samples

numBounces

Vector of bounce counts per sample (if requested)

bounceDistances

List of bounce distances per sample (if requested)

References

Pakman, A. and Paninski, L. (2014). Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians. Journal of Computational and Graphical Statistics. doi:10.1080/10618600.2013.788448

Examples

set.seed(1)
d <- 10
A <- matrix(runif(d^2)*2 - 1, ncol=d)
precMat <- t(A) %*% A
R <- cholesky(precMat)
mu <- rep(0, d)
constrainDirec <- diag(d)
constrainBound <- rep(0,d)
initial <- rep(1, d)
results <- harmonicHMC(1000, 1000, mu, R, constrainDirec, constrainBound, initial, precFlg = TRUE)
set.seed(1)
d <- 10
A <- matrix(runif(d^2)*2 - 1, ncol=d)
precMat <- t(A) %*% A
R <- cholesky(precMat)
mu <- rep(0, d)
constrainDirec <- diag(d)
constrainBound <- rep(0,d)
initial <- rep(1, d)
results <- harmonicHMC(1000, 1000, mu, R, constrainDirec, constrainBound, initial, precFlg = TRUE)

Markovian Zigzag Sampler

Description

Sample from a truncated multivariate normal distribution using the Markovian Zigzag process, a continuous-time, non-reversible Markov chain Monte Carlo method based on piecewise deterministic Markov processes (PDMPs).

Usage

markovianZigzag(
  nSample,
  burnin = 0,
  mean,
  prec,
  lowerBounds,
  upperBounds,
  init = NULL,
  stepSize = NULL,
  seed = 1,
  diagnosticMode = FALSE,
  nStatusUpdate = 0L
)
markovianZigzag(
  nSample,
  burnin = 0,
  mean,
  prec,
  lowerBounds,
  upperBounds,
  init = NULL,
  stepSize = NULL,
  seed = 1,
  diagnosticMode = FALSE,
  nStatusUpdate = 0L
)

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 the Markovian Zigzag sampler. Default value is the empirically optimal choice: $\sqrt{2}\lambda^{-1/2}$ , where $\lambda$ is the minimal eigenvalue of the precision matrix.

seed

Random seed (default = 1).

diagnosticMode

Logical. TRUE for also returning diagnostic information such as the step size used.

nStatusUpdate

Number of status updates to print during sampling. If 0 (default), no updates are printed.

Value

An nSample-by-d matrix of samples. If diagnosticMode is TRUE, a list with additional diagnostic information is returned.

References

Bierkens, J., Roberts, G. O., and Zitt, P.-A. (2019). Ergodicity of the zigzag process. The Annals of Applied Probability, 29(4): 2266-2301.

Examples

set.seed(1)
d <- 5
A <- matrix(runif(d^2)*2-1, ncol=d)
precMat <- t(A) %*% A
initial <- rep(1, d)
results <- markovianZigzag(
  nSample = 1000,
  burnin = 1000,
  mean = rep(0, d),
  prec = precMat,
  lowerBounds = rep(0, d),
  upperBounds = rep(Inf, d)
)
set.seed(1)
d <- 5
A <- matrix(runif(d^2)*2-1, ncol=d)
precMat <- t(A) %*% A
initial <- rep(1, d)
results <- markovianZigzag(
  nSample = 1000,
  burnin = 1000,
  mean = rep(0, d),
  prec = precMat,
  lowerBounds = rep(0, d),
  upperBounds = rep(Inf, d)
)

Set the mean for the target MTN

Description

Set the mean vector for a given Zigzag-HMC engine object.

Usage

setMean(engine, mean)
setMean(engine, mean)

Arguments

engine

A Zigzag-HMC engine container object.

mean

the mean vector.

Examples

# First create an engine
engine <- createEngine(dimension = 2, 
                       lowerBounds = c(-1, -1),
                       upperBounds = c(1, 1),
                       seed = 123,
                       mean = c(0, 0),
                       precision = diag(2))
# Update the mean
setMean(engine, mean = c(0.5, 0.5))
# First create an engine
engine <- createEngine(dimension = 2, 
                       lowerBounds = c(-1, -1),
                       upperBounds = c(1, 1),
                       seed = 123,
                       mean = c(0, 0),
                       precision = diag(2))
# Update the mean
setMean(engine, mean = c(0.5, 0.5))

Set the precision matrix for the target MTN

Description

Set the precision matrix for a given Zigzag-HMC engine object.

Usage

setPrecision(engine, precision)
setPrecision(engine, precision)

Arguments

engine

A Zigzag-HMC engine container object.

precision

the precision matrix.

Examples

# First create an engine
engine <- createEngine(dimension = 2,
                       lowerBounds = c(-1, -1),
                       upperBounds = c(1, 1),
                       seed = 123,
                       mean = c(0, 0),
                       precision = diag(2))
# Update with a correlated precision matrix
new_precision <- matrix(c(2, 0.8, 0.8, 2), nrow = 2)
setPrecision(engine, precision = new_precision)
# First create an engine
engine <- createEngine(dimension = 2,
                       lowerBounds = c(-1, -1),
                       upperBounds = c(1, 1),
                       seed = 123,
                       mean = c(0, 0),
                       precision = diag(2))
# Update with a correlated precision matrix
new_precision <- matrix(c(2, 0.8, 0.8, 2), nrow = 2)
setPrecision(engine, precision = new_precision)

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

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))

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))

Package 'hdtg'

Help Index

Efficient Cholesky decomposition

Description

Usage

Arguments

Value

See Also

Examples

Create a Zigzag-HMC engine object

Description

Usage

Arguments

Value

See Also

Examples

Create a Zigzag-NUTS engine object

Description

Usage

Arguments

Value

See Also

Examples

Draw a random Laplace momentum

Description

Usage

Arguments

Value

See Also

Examples

One-step Harmonic HMC Sampler (Whitened Coordinates)

Description

Usage

Arguments

See Also

Examples

Get an eligible initial value for a MTN with given mean and truncations

Description

Usage

Arguments

Value

See Also

Examples

Draw one Markovian zigzag sample

Description

Usage

Arguments

Value

See Also

Examples

Draw one MTN sample with Zigzag-HMC or Zigzag-NUTS

Description

Usage

Arguments

Value

Note

See Also

Examples

Sample from a truncated Gaussian distribution with the harmonic HMC

Description

Usage

Arguments

Value

References

See Also

Examples

Markovian Zigzag Sampler

Description

Usage

Arguments

Value

References

See Also

Examples

Set the mean for the target MTN

Description

Usage

Arguments

See Also

Examples