coda: gelman.plot – R documentation

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coda

gelman.plot

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.