Gelfand.Diagnostic {LaplacesDemon}  R Documentation 
Gelfand's Convergence Diagnostic
Description
Gelfand et al. (1990) proposed a convergence diagnostic for Markov
chains. The Gelfand.Diagnostic
function is an interpretation of
Gelfand's “thick felttip 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 burnin
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, felttip
pen. This depends on the size of the plot, and, of course, the
pen. The estimated width of a “thick felttip pen” is included as a
black, vertical line. The pen in Gelfand.Diagnostic
is included
for historical reasons. This diagnostic requires numerous samples.
Usage
Gelfand.Diagnostic(x, k=3, pen=FALSE)
Arguments
x 
This required argument is a vector of marginal posterior
samples, such as selected from the output of

k 
This argument specifies the number 
pen 
Logical. This argument defaults to 
Value
The Gelfand.Diagnostic
returns a plot.
Author(s)
Statisticat, LLC. software@bayesianinference.com
References
Gelfand, A.E., Hills, S., RacinePoon, 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.
See Also
burnin
and
LaplacesDemon
.
Examples
library(LaplacesDemon)
x < rnorm(1000)
Gelfand.Diagnostic(x)