Estimate the effective sample size (ESS) of a Markov chain as described in Gong and Flegal (2015).
ess(x, g = NULL, ...)The function returns the estimated effective sample size for each component of g.
a matrix or data frame of Markov chain output. Number of rows is the Monte Carlo sample size.
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.
arguments passed on to the mcse.mat function. For example method = “tukey” and size =
“cuberoot” can be used.
ESS is the size of an iid sample with the same variance as the current sample for estimating the expectation of g. ESS is given by $$ESS = n \frac{\lambda^{2}}{\sigma^{2}}$$ where \(\lambda^{2}\) is the sample variance and \(\sigma^{2}\) is an estimate of the variance in the Markov chain central limit theorem. The denominator by default is a batch means estimator, but the default can be changed with the `method` argument.
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, 25, 684-700.
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.