ess {batchmeans}

Estimate effective sample size (ESS) as described in Kass et al. (1998) and Robert and Casella (2004; p. 500).

Description

Estimate effective sample size (ESS) as described in Kass et al. (1998) and Robert and Casella (2004; p. 500).

Usage

ess(x, imse = TRUE, verbose = FALSE)

Arguments

x

a vector of values from a Markov chain.

imse

logical. If TRUE, use an approach that is analogous to Geyer's initial monotone positive sequence estimator (IMSE), where correlations beyond a certain lag are removed to reduce noise.

verbose

logical. If TRUE and imse = TRUE, inform about the lag at which truncation occurs, and warn if the lag is probably too small.

Details

ESS is the size of an iid sample with the same variance as the current sample. ESS is given by

\mbox{ESS}=T/\eta,

where

\eta=1+2\sum \mbox{all lag autocorrelations}.

Value

The function returns the estimated effective sample size.

References

Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. (1998) Markov chain Monte Carlo in practice: A roundtable discussion. The American Statistician, 52, 93–100.

Robert, C. P. and Casella, G. (2004) Monte Carlo Statistical Methods. New York: Springer.

Geyer, C. J. (1992) Practical Markov chain Monte Carlo. Statistical Science, 7, 473–483.