ESS: Effective Sample Size (ESS)

In astsa: Applied Statistical Time Series Analysis

Effective Sample Size (ESS)

Description

Estimates the ESS of a given vector of samples.

Usage

ESS(trace, tol = 1e-08, BIC = TRUE, digits=2)

Arguments

trace	vector of sampled values from an MCMC run (univariate only)
tol	ESS is returned as zero if the estimated spectrum at frequency zero is less than this value
BIC	if TRUE (default), spec0 is obtained using BIC; otherwise, AIC is used. See the details.
digits	integer indicating the approximate number of decimal places to be used

Details

Uses spec.ic to estimate the spectrum of the input at frequency zero (spec0). Then, ESS is estimated as ESS = length(trace)*var(trace)/spec0. See Examples for multivariate case.

ESS is discussed in detail in Example 6.31 of Time Series Analysis and Its Applications: With R Examples (5th ed, 2025).

Value

Returns the estimated ESS of the input.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# How autocorrelation affects ESS
x   = matrix(NA, 500, 3)  # sample size is 500
phi = c(0,.3,.9)          # no, low, high
for (i in 1:3) x[,i] = sarima.sim(ar=phi[i])
apply(x, 2, ESS, digits=-1)

astsa documentation built on Aug. 21, 2025, 5:47 p.m.