gelman.plot {coda}

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+bin.width), the third contains samples 1:(50+2*bin.width) and so on. If the chain has less than 50 + bin.width iterations then gelman.diag will exit with an error.

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.