R: Gelman-Rubin-Brooks plot

gelman.plot {coda} | R Documentation

## Gelman-Rubin-Brooks plot

### Description

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

### 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

`gelman.diag`.

[Package coda version 0.19-1 Index]