Metropolis-Coupled Hamiltonian Monte Carlo (MCHMC)

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

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.

Value

A named list containing

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')
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
Acceptance Ratio: The proportion of proposals that were accepted (for each chain).
Beta Values: The set of temperatures used in each chain
Swap History: the history of chain swaps
Swap Acceptance Ratio: The ratio of swap acceptances

Details

Metropolis-Coupled HMC does not support discrete distributions.

This algorithm has been used to model human data in Castillo et al. (2024) .

References

Castillo L, León-Villagrá P, Chater N, Sanborn A (2024). “Explaining the Flaws in Human Random Generation as Local Sampling with Momentum.” PLOS Computational Biology, 20(1), 1–24. doi:10.1371/journal.pcbi.1011739 .

Examples


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