Gelfand et al. (1990) proposed a convergence diagnostic for Markov
Gelfand.Diagnostic function is an interpretation of
Gelfand's “thick felt-tip pen” MCMC convergence diagnostic. This
diagnostic plots a series of kernel density plots at k
intervals of cumulative samples. Given a vector of S samples
from a marginal posterior distribution, theta, multiple
kernel density lines are plotted together, where each includes samples
from a different interval. It is assumed that
iterations have been discarded.
Gelfand et al. (1990) assert that convergence is violated when the
plotted lines are farther apart than the width of a thick, felt-tip
pen. This depends on the size of the plot, and, of course, the
pen. The estimated width of a “thick felt-tip pen” is included as a
black, vertical line. The pen in
Gelfand.Diagnostic is included
for historical reasons. This diagnostic requires numerous samples.
This required argument is a vector of marginal posterior
samples, such as selected from the output of
This argument specifies the number k of kernel density plots given cumulative intervals of samples. This argument defaults to k=3.
Logical. This argument defaults to
Gelfand.Diagnostic returns a plot.
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Gelfand, A.E., Hills, S., Racine-Poon, A., and Smith, A.F.M. (1990). "Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling". Journal of the American Statistical Association, 85, p. 972–985.
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