sampler_mchmc: Metropolis-Coupled Hamiltonian Monte Carlo (MCHMC)

In samplr: Compare Human Performance to Sampling Algorithms

Metropolis-Coupled Hamiltonian Monte Carlo (MCHMC)

Description

Metropolis-Coupled version of HMC, i.e. running multiple chains at different temperatures which stochastically swap positions.

Usage

sampler_mchmc(
  start,
  distr_name = NULL,
  distr_params = NULL,
  epsilon = 0.5,
  L = 10,
  nChains = 6,
  delta_T = 4,
  swap_all = TRUE,
  iterations = 1024L,
  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
nChains	Number of chains to run.
delta_T	numeric, >1. Temperature increment parameter. The bigger this number, the steeper the increase in temperature between the cold chain and the next chain
swap_all	Boolean. If true, every iteration attempts floor(nChains / 2) swaps. If false, only one swap 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

Metropolis-Coupled HMC does not support discrete distributions.

This algorithm has been used to model human data in \insertCitecastillo2024ExplainingFlawsHuman;textualsamplr.

Value

A named list containing

1. Samples: the history of visited places (an n x d x c array, n = iterations; d = dimensions; c = chain index, with c==1 being the 'cold chain')

2. Momentums: the history of momentum values (an n x d x c array, n = iterations; d = dimensions; c = chain index, with c==1 being the 'cold chain'). 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 (for each chain).

4. Beta Values: The set of temperatures used in each chain

5. Swap History: the history of chain swaps

6. Swap Acceptance Ratio: The ratio of swap acceptances

References

\insertAllCited

Examples

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

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