samplesBgr: Plot the Gelman-Rubin convergence statistic

Description

This function calculates and plots the Gelman-Rubin convergence statistic, as modified by Brooks and Gelman (1998).

Usage

samplesBgr(node, beg = samplesGetBeg(), end = samplesGetEnd(), 
    firstChain = samplesGetFirstChain(), 
    lastChain = samplesGetLastChain(), thin = samplesGetThin(),
    bins = 50, plot = TRUE, mfrow = c(3, 2), ask = NULL, 
    ann = TRUE, ...)

Arguments

node

Character vector of length 1, name of a variable in the model.

beg, end

Arguments to select a slice of monitored values corresponding to iterations beg:end.

firstChain, lastChain

Arguments to select a sub group of chains to calculate the Gelman-Rubin convergence statistics for. Number of chains must be larger than one.

thin

Only use every thin-th value of the stored sample for statistics.

bins

Number of blocks

plot

Logical, whether to plot the BGR statistics or only return the values. If TRUE, values are returned invisibly.

mfrow, ask, ann

Graphical parameters, see par for details. ask defaults to TRUE unless it is plotting into an already opened non-interactive device. The ann parameter is not ava

...

Further graphical parameters as in par may also be passed as arguments to plotBgr.

Value

A list containing data frames - one for each scalar variable contained in argument node. Each data frames contains elements
Iterationend iteration of corresponding bin
pooledChain80pct)80pct interval (normalized) of pooled chains
withinChain80pct80pct interval (normalized) of mean within chain
bgrRatioBGR ratio

Details

The width of the central 80% interval of the pooled runs is green, the average width of the 80% intervals within the individual runs is blue, and their ratio $R (= pooled / within)$ is red. For plotting purposes the pooled and within interval widths are normalised to have an overall maximum of one. The statistics are calculated in bins of length 50: $R$ would generally be expected to be greater than 1 if the starting values are suitably over-dispersed. Brooks and Gelman (1998) emphasise that one should be concerned both with convergence of $R$ to 1, and with convergence of both the pooled and within interval widths to stability. If the variable of interest is an array, slices of the array can be selected using the notation variable[lower0:upper0, lower1:upper1, ...]. A star * can be entered as shorthand for all the stored samples. If the arguments are left at their defaults the whole sample for all chains will be used for calculation.

References

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