bimodal_barker_proposal: Create a new Barker proposal object with bimodal noise...

In rmcmc: Robust Markov Chain Monte Carlo Methods

Create a new Barker proposal object with bimodal noise distribution.

Description

Convenience function for creating a Barker proposal with bimodal auxiliary noise variable distribution, corresponding to equally-weighted normal components with shared variance sigma and means ⁠±sqrt(1 - sigma^2)⁠. This choice of noise distribution was suggested in Vogrinc et al. (2023) and found to give improved performance over the default choice of a standard normal auxiliary noise distribution in a range of targets.

Usage

bimodal_barker_proposal(
  sigma = 0.1,
  scale = NULL,
  shape = NULL,
  sample_uniform = stats::runif
)

Arguments

sigma	Standard deviation of equally-weighted normal components in bimodal auxiliary noise distribution, with corresponding means of ⁠±sqrt(1 - sigma^2)⁠.
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_uniform	Function which generates a random vector from standard uniform distribution given an integer size.

Details

For more details see the vignette: vignette("adjusting-noise-distribution", 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

Vogrinc, J., Livingstone, S., & Zanella, G. (2023). Optimal design of the Barker proposal and other locally balanced Metropolis–Hastings algorithms. Biometrika, 110(3), 579-595.

See Also

barker_proposal()

Examples

target_distribution <- list(
  log_density = function(x) -sum(x^2) / 2,
  gradient_log_density = function(x) -x
)
proposal <- bimodal_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.