batchmeans (version 1.0-1)

ess: 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.

Value

• The function returns the estimated effective sample size.

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

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.