langevin_proposal: Create a new Langevin proposal object.

In rmcmc: Robust Markov Chain Monte Carlo Methods

Create a new Langevin proposal object.

Description

The Langevin proposal is a gradient-based proposal corresponding to a Euler-Maruyama time discretisation of a Langevin diffusion.

Usage

langevin_proposal(scale = NULL, shape = NULL, sample_auxiliary = stats::rnorm)

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.

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

Besag, J. (1994). "Comments on "Representations of knowledge in complex systems" by U. Grenander and MI Miller". Journal of the Royal Statistical Society, Series B. 56: 591–592.

Roberts, G. O., & Tweedie, R. L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2 (4), 341 - 363.

Examples

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