Gelfand et al. (1990) proposed a convergence diagnostic for Markov
chains. The `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 `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, 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.

`Gelfand.Diagnostic(x, k=3, pen=FALSE)`

x

This required argument is a vector of marginal posterior
samples, such as selected from the output of
`LaplacesDemon`

.

k

This argument specifies the number \(k\) of kernel density plots given cumulative intervals of samples. This argument defaults to \(k=3\).

pen

Logical. This argument defaults to `pen=FALSE`

. When
`pen=TRUE`

, the thick felt-tip pen is included as a black,
vertical line.

The `Gelfand.Diagnostic`

returns a plot.

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.

`burnin`

and
`LaplacesDemon`

.

```
# NOT RUN {
library(LaplacesDemon)
x <- rnorm(1000)
Gelfand.Diagnostic(x)
# }
```

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