sampler_hmc: Hamiltonian Monte-Carlo Sampler (HMC)

In samplr: Compare Human Performance to Sampling Algorithms

Hamiltonian Monte-Carlo Sampler (HMC)

Description

Hamiltonian Monte-Carlo, also called Hybrid Monte Carlo, is a sampling algorithm that uses Hamiltonian Dynamics to approximate a posterior distribution. Unlike MH and MC3, HMC uses not only the current position, but also a sense of momentum, to draw future samples. An introduction to HMC can be read in \insertCitebetancourt2018ConceptualIntroductionHamiltonian;textualsamplr.

Usage

sampler_hmc(
  start,
  distr_name = NULL,
  distr_params = NULL,
  epsilon = 0.5,
  L = 10,
  iterations = 1024,
  weights = NULL,
  custom_density = NULL
)

Arguments

start	Vector. Starting position of the sampler.
distr_name	Name of the distribution from which to sample from.
distr_params	Distribution parameters.
epsilon	Size of the leapfrog step
L	Number of leapfrog steps per iteration
iterations	Number of iterations of the sampler.
weights	If using a mixture distribution, the weights given to each constituent distribution. If none given, it defaults to equal weights for all distributions.
custom_density	Instead of providing names, params and weights, the user may prefer to provide a custom density function.

Details

This implementations assumes that the momentum is drawn from a normal distribution with mean 0 and identity covariance matrix (p ~ N (0, I)). Hamiltonian Monte Carlo does not support discrete distributions.

This algorithm has been used to model human data in \insertCiteaitchison2016HamiltonianBrainEfficient;textualsamplr, \insertCitecastillo2024ExplainingFlawsHuman;textualsamplr and \insertCitezhu2022UnderstandingStructureCognitive;textualsamplr among others.

Value

A named list containing

1. Samples: the history of visited places (an n x d matrix, n = iterations; d = dimensions)

2. Momentums: the history of momentum values (an n x d matrix, n = iterations; d = dimensions). Nothing is proposed in the first iteration (the first iteration is the start value) and so the first row is NA

3. Acceptance Ratio: The proportion of proposals that were accepted.

References

\insertAllCited

Examples

result <- sampler_hmc(
    distr_name = "norm", distr_params = c(0,1), 
    start = 1, epsilon = .01, L = 100
    )
cold_chain <- result$Samples

samplr documentation built on April 4, 2025, 12:30 a.m.