Plot KL Divergence of Predictive Density to Assess Convergence of Bayesian Non-Parametric DPMM Sampler

This plots the Kullback-Leibler (KL) divergence between a fixed (initial/baseline) predictive density and the predictive density calculated from later individual realisations in the MCMC run of one of the Bayesian non-parametric summarisation approach. The divergence from the initial predictive density is plotted as a function of the realisation/iteration number.

This aims to identify when the divergence, from the initial estimate of the shared \(f(\theta)\) to the current estimate, has begun to stabilise. Hence, to (informally) assess when the MCMC chain has converged to equilibrium for the shared, underlying, predictive \(f(\theta)\).

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

Usage

PlotConvergenceData(output_data, n_initial = NA)

Arguments

output_data

The return value from one of the Bayesian non-parametric DPMM summarisation functions, i.e., PolyaUrnBivarDirichlet or WalkerBivarDirichlet.

n_initial

The number of (thinned) realisations to use for the 'initial' predictive shared density. This predictive density is then compared with the predictive obtained at each subsequent realisation in the (thinned) DPMM output. If not specified, then the minimum of 1000 realisations, or 1 / 10 of the total number of realisations, will be used.

Value

None

Examples

# Plot results for the example two_normal data
# NOTE: This does not show meaningful results as n_iter
# is too small. Try increasing n_iter to 1e5.
polya_urn_output <- PolyaUrnBivarDirichlet(
    two_normals$c14_age,
    two_normals$c14_sig,
    intcal20,
    n_iter = 500,
    show_progress = FALSE)
PlotConvergenceData(polya_urn_output)