# ess

0th

Percentile

##### Estimate effective sample size (ESS) as described in Gong and Felgal (2015).

Estimate effective sample size (ESS) as described in Gong and Flegal (2015).

##### Usage
ess(x, g = NULL, ...)
##### Arguments
x

a matrix or data frame of Markov chain output. Number of rows is the Monte Carlo sample size.

...

arguments passed on to the mcse.mat function. For example method = "tukey" and size = "cuberoot" can be used.

g

a function that represents features of interest. g is applied to each row of x and thus g should take a vector input only. If g is NULL, g is set to be identity, which is estimation of the mean of the target density.

##### Details

ESS is the size of an iid sample with the same variance as the current sample. ESS is given by $$\mbox{ESS}=n \frac{\lambda^2}{\sigma^2},$$ where $\lambda^2$ is the sample variance and $\sigma^2$ is an estimate of the variance in the CLT. This is by default the batch means estimator, but the default can be changed with the method argument.

##### Value

The function returns the estimated effective sample size.

##### References

Gong, L. and Flegal, J. M. (2015) A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo Journal of Computational and Graphical Statistics.

minESS, which calculates the minimum effective samples required for the problem.
multiESS, which calculates multivariate effective sample size using a Markov chain and a function g.