# ess

##### 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*.

##### See Also

`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.

*Documentation reproduced from package mcmcse, version 1.3-2, License: GPL (>= 2)*