Conduct a within-chain step of the ptMCMC algorithm

This set of functions steps the chains forward one iteration of the within-chain component of the ptMCMC algorithm. step_chains is the main function, comprised of a proposal (made by prop_step), an evaluation of that proposal (made by eval_step), and then an update of the configuration (made by take_step).

This set of functions was designed to work within TS and specifically est_changepoints. They are still hardcoded to do so, but have the capacity to be generalized to work with any estimation via ptMCMC with additional coding work.

step_chains(i, cpts, inputs)

propose_step(i, cpts, inputs)

eval_step(i, cpts, prop_step, inputs)

take_step(cpts, prop_step, accept_step)

Arguments

i	integer iteration index.
cpts	matrix of change point locations across chains.
inputs	Class ptMCMC_inputs list, containing the static inputs for use within the ptMCMC algorithm.
prop_step	Proposed step output from propose_step.
accept_step	logical indicator of acceptance of each chain's proposed step.

Value

step_chains: list of change points, log-likelihoods, and logical indicators of acceptance for each chain.

propose_step: list of change points and log-likelihood values for the proposal.

eval_step: logical vector indicating if each chain's proposal was accepted.

take_step: list of change points, log-likelihoods, and logical indicators of acceptance for each chain.

Details

For each iteration of the ptMCMC algorithm, all of the chains have the potential to take a step. The possible step is proposed under a proposal distribution (here for change points we use a symmetric geometric distribution), the proposed step is then evaluated and either accepted or not (following the Metropolis-Hastings rule; Metropolis, et al. 1953, Hasting 1960, Gupta et al. 2018), and then accordingly taken or not (the configurations are updated).

References

Gupta, S., L. Hainsworth, J. S. Hogg, R. E. C. Lee, and J. R. Faeder. 2018. Evaluation of parallel tempering to accelerate Bayesian parameter estimation in systems biology. link.

Hastings, W. K. 1970. Monte Carlo sampling methods using Markov Chains and their applications. Biometrika 57:97-109. link.

Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equations of state calculations by fast computing machines. Journal of Chemical Physics 21: 1087-1092. link.

Examples

# \donttest{
  data(rodents)
  document_term_table <- rodents$document_term_table
  document_covariate_table <- rodents$document_covariate_table
  LDA_models <- LDA_set(document_term_table, topics = 2)[[1]]
  data <- document_covariate_table
  data$gamma <- LDA_models@gamma
  weights <- document_weights(document_term_table)
  data <- data[order(data[,"newmoon"]), ]
  saves <- prep_saves(1, TS_control())
  inputs <- prep_ptMCMC_inputs(data, gamma ~ 1, 1, "newmoon", weights,
                               TS_control())
  cpts <- prep_cpts(data, gamma ~ 1, 1, "newmoon", weights, TS_control())
  ids <- prep_ids(TS_control())
  for(i in 1:TS_control()$nit){
    steps <- step_chains(i, cpts, inputs)
    swaps <- swap_chains(steps, inputs, ids)
    saves <- update_saves(i, saves, steps, swaps)
    cpts <- update_cpts(cpts, swaps)
    ids <- update_ids(ids, swaps)
  }
  # within step_chains()
  cpts <- prep_cpts(data, gamma ~ 1, 1, "newmoon", weights, TS_control())
  i <- 1
  prop_step <- propose_step(i, cpts, inputs)
  accept_step <- eval_step(i, cpts, prop_step, inputs)
  take_step(cpts, prop_step, accept_step)
# }