Parallel Merge-Split/Recombination MCMC Redistricting Sampler — redist_mergesplit

redist_mergesplit_parallel() runs redist_mergesplit() on several chains in parallel.

redist_mergesplit_parallel(
  map,
  nsims,
  chains = 1,
  warmup = if (is.null(init_plan)) 10 else max(100, nsims%/%5),
  thin = 1L,
  init_plan = NULL,
  counties = NULL,
  compactness = 1,
  constraints = list(),
  constraint_fn = function(m) rep(0, ncol(m)),
  adapt_k_thresh = 0.99,
  k = NULL,
  ncores = NULL,
  cl_type = "PSOCK",
  return_all = TRUE,
  init_name = NULL,
  verbose = FALSE,
  silent = FALSE
)

Arguments

map: A redist_map object.
nsims: The number of samples to draw, including warmup.
chains: the number of parallel chains to run. Each chain will have nsims draws. If init_plan is sampled, each chain will be initialized with its own sampled plan.
warmup: The number of warmup samples to discard. Recommended to be at least the first 20% of samples, and in any case no less than around 100 samples, unless initializing from a random plan.
thin: Save every thin-th sample. Defaults to no thinning (1).
init_plan: The initial state of the map, provided as a single vector to be shared across all chains, or a matrix with chains columns. If not provided, will default to the reference map of the map object, or if none exists, will sample a random initial state using redist_smc. You can also request a random initial state for each chain by setting init_plan="sample".
counties: A vector containing county (or other administrative or geographic unit) labels for each unit, which may be integers ranging from 1 to the number of counties, or a factor or character vector. If provided, the algorithm will generate maps tend to follow county lines. There is no strength parameter associated with this constraint. To adjust the number of county splits further, or to constrain a second type of administrative split, consider using add_constr_splits(), add_constr_multisplits(), and add_constr_total_splits().
compactness: Controls the compactness of the generated districts, with higher values preferring more compact districts. Must be nonnegative. See the 'Details' section for more information, and computational considerations.
constraints: A list containing information on constraints to implement. See the 'Details' section for more information.
constraint_fn: A function which takes in a matrix where each column is a redistricting plan and outputs a vector of log-weights, which will be added the the final weights.
adapt_k_thresh: The threshold value used in the heuristic to select a value k_i for each splitting iteration. Set to 0.9999 or 1 if the algorithm does not appear to be sampling from the target distribution. Must be between 0 and 1.
k: The number of edges to consider cutting after drawing a spanning tree. Should be selected automatically in nearly all cases.
ncores: the number of parallel processes to run. Defaults to the maximum available.
cl_type: the cluster type (see makeCluster()). Safest is "PSOCK", but "FORK" may be appropriate in some settings.
return_all: if TRUE return all sampled plans; otherwise, just return the final plan from each chain.
init_name: a name for the initial plan, or FALSE to not include the initial plan in the output. Defaults to the column name of the existing plan, or "<init>" if the initial plan is sampled.
verbose: Whether to print out intermediate information while sampling. Recommended.
silent: Whether to suppress all diagnostic information.

Value

A redist_plans object with all of the simulated plans, and an additional chain column indicating the chain the plan was drawn from.

Details

This function draws samples from a specific target measure, controlled by the map, compactness, and constraints parameters.

Key to ensuring good performance is monitoring the acceptance rate, which is reported at the sample level in the output. Users should also check diagnostics of the sample by running summary.redist_plans().

Higher values of compactness sample more compact districts; setting this parameter to 1 is computationally efficient and generates nicely compact districts.

References

Carter, D., Herschlag, G., Hunter, Z., and Mattingly, J. (2019). A merge-split proposal for reversible Monte Carlo Markov chain sampling of redistricting plans. arXiv preprint arXiv:1911.01503.

McCartan, C., & Imai, K. (2023). Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans. Annals of Applied Statistics 17(4). Available at doi:10.1214/23-AOAS1763 .

DeFord, D., Duchin, M., and Solomon, J. (2019). Recombination: A family of Markov chains for redistricting. arXiv preprint arXiv:1911.05725.

Examples

if (FALSE) {
data(fl25)
fl_map <- redist_map(fl25, ndists = 3, pop_tol = 0.1)
sampled <- redist_mergesplit_parallel(fl_map, nsims = 100, chains = 100)
}