# gelman.plot

##### 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. - ask
- 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.

##### See Also

*Documentation reproduced from package coda, version 0.17-1, License: GPL (>= 2)*