# gelman.plot

0th

Percentile

##### Gelman-Rubin-Brooks plot

This plot shows the evolution of Gelman and Rubin's shrink factor as the number of iterations increases.

Keywords
hplot
##### Usage
gelman.plot(x, bin.width = 10, max.bins = 50,
confidence = 0.95, transform = FALSE, autoburnin=TRUE, auto.layout = TRUE,
ask, col, lty, xlab, ylab, type, ...)
##### Arguments
x
an mcmc object
bin.width
Number of observations per segment, excluding the first segment which always has at least 50 iterations.
max.bins
Maximum number of bins, excluding the last one.
confidence
Coverage probability of confidence interval.
transform
Automatic variable transformation (see gelman.diag)
autoburnin
Remove first half of sequence (see gelman.diag)
auto.layout
If TRUE then, set up own layout for plots, otherwise use existing one.
Prompt user before displaying each page of plots. Default is dev.interactive() in R and interactive() in S-PLUS.
col
graphical parameter (see par)
lty
graphical parameter (see par)
xlab
graphical parameter (see par)
ylab
graphical parameter (see par)
type
graphical parameter (see par)
...
further graphical parameters.
##### Details

The Markov chain is divided into bins according to the arguments bin.width and max.bins. Then the Gelman-Rubin shrink factor is repeatedly calculated. The first shrink factor is calculated with observations 1:50, the second with observations $1:(50+n)$ where n is the bin width, the third contains samples $1:(50+2n)$ and so on.

##### Theory

A potential problem with gelman.diag is that it may mis-diagnose convergence if the shrink factor happens to be close to 1 by chance. By calculating the shrink factor at several points in time, gelman.plot shows if the shrink factor has really converged, or whether it is still fluctuating.

##### References

Brooks, S P. and Gelman, A. (1998) General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics, 7, 434-455.

gelman.diag.