barker_proposal: Create a new Barker proposal object.

In rmcmc: Robust Markov Chain Monte Carlo Methods

Create a new Barker proposal object.

Description

The Barker proposal is a gradient-based proposal inspired by the Barker accept-reject rule and proposed in Livingstone and Zanella (2022). It offers improved robustness compared to alternative gradient-based proposals such as Langevin proposals.

Usage

barker_proposal(
  scale = NULL,
  shape = NULL,
  sample_auxiliary = stats::rnorm,
  sample_uniform = stats::runif
)

Arguments

scale	Scale parameter of proposal distribution. A non-negative scalar value determining scale of steps proposed.
shape	Shape parameter of proposal distribution. Either a vector corresponding to a diagonal shape matrix with per-dimension scaling factors, or a matrix allowing arbitrary linear transformations.
sample_auxiliary	Function which generates a random vector from auxiliary variable distribution.
sample_uniform	Function which generates a random vector from standard uniform distribution given an integer size.

Details

For more details see the vignette: vignette("barker-proposal", package = "rmcmc")

Value

Proposal object. A list with entries

• sample: a function to generate sample from proposal distribution given current chain state,

• log_density_ratio: a function to compute log density ratio for proposal for a given pair of current and proposed chain states,

• update: a function to update parameters of proposal,

• parameters: a function to return list of current parameter values.

• default_target_accept_prob: a function returning the default target acceptance rate to use for any scale adaptation.

• default_initial_scale: a function which given a dimension gives a default value to use for the initial proposal scale parameter.

References

Livingstone, S., & Zanella, G. (2022). The Barker proposal: combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(2), 496-523.

Examples

target_distribution <- list(
  log_density = function(x) -sum(x^2) / 2,
  gradient_log_density = function(x) -x
)
proposal <- barker_proposal(scale = 1.)
state <- chain_state(c(0., 0.))
withr::with_seed(
  876287L, proposed_state <- proposal$sample(state, target_distribution)
)
log_density_ratio <- proposal$log_density_ratio(
  state, proposed_state, target_distribution
)
proposal$update(scale = 0.5)

rmcmc documentation built on April 3, 2025, 5:27 p.m.