mcmc function

Utility functions for MCMC output analysis

Returns the mean, the standard deviation of the mean, and a sequence of partial means of the input vector or matrix.

mcmcMean(x, sd = TRUE)
mcmcMeans(x, sd = TRUE)
mcmcSD(x)
ergMean(x, m = 1)

Arguments

• x: vector or matrix containing the output of a Markov chain Monte Carlo simulation.
• sd: logical: should an estimate of the Monte Carlo standard deviation be reported?
• m: ergodic means are computed for i in m:NROW(x)

Details

The argument x is typically the output from a simulation. If a matrix, rows are considered consecutive simulations of a target vector. In this case means, standard deviations, and ergodic means are returned for each column. The standard deviation of the mean is estimated using Sokal's method (see the reference). mcmcMeans

is an alias for mcmcMean.

Returns

mcmcMean returns the sample mean of a vector containing the output of an MCMC sampler, together with an estimated standard error. If the input is a matrix, means and standard errors are computed for each column.

mcmcSD returns an estimate of the standard deviation of the mean for the output of an MCMC sampler.

ergMean returns a vector of running ergodic means.

References

P. Green (2001). A Primer on Markov Chain Monte Carlo. In Complex Stochastic Systems, (Barndorff-Nielsen, Cox and Kl"uppelberg, eds.). Chapman and Hall/CRC.

Author(s)

Giovanni Petris GPetris@uark.edu

Examples

x <- matrix(rexp(1000), nc=4)
dimnames(x) <- list(NULL, LETTERS[1:NCOL(x)])
mcmcSD(x)
mcmcMean(x)
em <- ergMean(x, m = 51)
plot(ts(em, start=51), xlab="Iteration", main="Ergodic means")