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)