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\name{batchSE}
\alias{batchSE}
\title{Batch Standard Error}
\description{
Effective standard deviation of population to produce the correct
standard errors.
}
\usage{
batchSE(x, batchSize=100)
}
\arguments{
\item{x}{An \code{mcmc} or \code{mcmc.list} object.}
\item{batchSize}{Number of observations to include in each batch.}
}
\details{
Because of the autocorrelation, the usual method of taking
\code{var(x)/n} overstates the precision of the estimate. This method
works around the problem by looking at the means of batches of the
parameter. If the batch size is large enough, the batch means should
be approximately uncorrelated and the normal formula for computing the
standard error should work.
The batch standard error procedure is usually thought to be not as
accurate as the time series methods used in \code{summary} and
\code{effectiveSize}. It is included here for completeness.
}
\value{
A vector giving the standard error for each column of \code{x}.
}
\references{
Roberts, GO (1996) Markov chain concepts related to sampling algorithms,
in Gilks, WR, Richardson, S and Spiegelhalter, DJ, \emph{Markov Chain
Monte Carlo in Practice}, Chapman and Hall, 45-58.
}
\seealso{
\code{\link{spectrum0.ar}}, \code{\link{effectiveSize}},
\code{\link{summary.mcmc}}
}
\author{Russell Almond}
\keyword{ts}
|
