sampler_mc3: Metropolis-coupled MCMC sampler (MC3)

In lucas-castillo/SampleR: Tools To Compare Human Performance To Sampling Algorithms

Description

This sampler is a variant of MCMC in which multiple parallel chains are run at different temperatures. The chains stochastically swap positions which allows the coldest chain to visit regions far from its starting point (unlike in MCMC). Because of this, an MC3 sampler can explore far-off regions, whereas an MCMC sampler may become stuck in a particular point of high density.

Usage

sampler_mc3(
  pdf,
  start,
  nChains = 6,
  iterations = 1024,
  sigma_prop = NULL,
  delta_T = 4,
  swap_all = TRUE
)

Arguments

pdf	Probability Density Function of the posterior distribution. Takes a vector as input
start	Vector. Starting point for the sampler
nChains	number of parallel chains to be run.
iterations	Numeric. Number of times the sampler runs
sigma_prop	Variance of the univariate proposal distribution. For multivariate proposals, covariance matrix of the proposal.
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.

Value

List with:

1. array of iterations x target_dimensions x nChains,

2. acceptance ratio for each chain,

3. history of swaps and

4. swap ratio.

If nChains == 1 items 3 and 4 are not returned

Examples

pdf_function <- function(x){return(mvtnorm::dmvnorm(x, mean = c(0,1), sigma = diag(2)))}
mc3_results <- sampler_mc3(
 pdf_function,
 start = c(0,0),
 iterations=10,
 nChains = 3,
 sigma_prop = diag(2) / 8
)

lucas-castillo/SampleR documentation built on Jan. 1, 2021, 8:25 a.m.