Plot Histogram of the Gelman-Rubin Convergence Diagnostic for Multiple Independent MCMC Chains

This plots a histogram of the potential scale reduction factors (PSRF) for each of the individual posterior calendar age estimates for multiple independent MCMC chains. Achieved by comparing the within-chain variance with the between-chains variance after n_burn iterations. The PSRF of each sample's posterior calendar age is calculated. If the chain have converged to the target posterior distribution, then PSRF should be close to 1 for all of the samples (a stringent condition is that all values are less than 1.1).

For more information read the vignette:
vignette("determining-convergence", package = "carbondate")

Usage

PlotGelmanRubinDiagnosticMultiChain(output_data_list, n_burn = NA)

Arguments

output_data_list

A list, each item containing the return value from one of the updating functions e.g. PolyaUrnBivarDirichlet, WalkerBivarDirichlet or PPcalibrate. The minimum number of elements in the list is 2.

n_burn

The number of MCMC iterations that should be discarded for burn-in. This relates to the total number of iterations n_iter when running the original update functions (not the thinned output_data). Any MCMC iterations before this are not used in the calculations of the PSRF. If not given, the first half of the MCMC chain is discarded. Note: The maximum value that the function will allow is n_iter - 100 * n_thin (where n_iter and n_thin are the arguments that were given to PPcalibrate) which would leave only 100 of the (thinned) values in output_data.

Value

None

Examples

# Plot results for the example data - n_iter is too small for convergence
# Try increasing n_iter to see the values of the PSRF decrease
po <- list()
for (i in 1:3) {
    set.seed(i)
    po[[i]] <- PolyaUrnBivarDirichlet(
        two_normals$c14_age,
        two_normals$c14_sig,
        intcal20,
        n_iter=400,
        show_progress = FALSE)
}
PlotGelmanRubinDiagnosticMultiChain(po)