The function calculates the minimum effective sample size required for a specified relative tolerance level. This function can also calculate the relative precision in estimation for a given estimated effective sample size.
minESS(p, alpha = .05, eps = .05, ess = NULL)By default function returns the minimum effective sample required for a given eps
tolerance. If ess is specified, then the value returned is the eps corresponding to that ess.
dimension of the estimation problem.
Confidence level.
Tolerance level. The eps value is ignored is ess is not NULL.
Estimated effective sample size. Usually the output value from multiESS.
The minimum effective samples required when estimating a vector of length p, with \(100(
1-\alpha)\%\) confidence and tolerance of \(\epsilon\) is $$mESS \geq \frac{2^{2/p} \pi}{(p
\Gamma(p/2))^{2/p}} \frac{\chi^{2}_{1-\alpha,p}}{\epsilon^{2}}.$$
The above equality can also be used to get \(\epsilon\) from an already obtained estimate of
mESS.
Gong, L., and Flegal, J. M. A practical sequential stopping rule for high-dimensional Markov chain Monte Carlo. Journal of Computational and Graphical Statistics, 25, 684-700.
Vats, D., Flegal, J. M., and, Jones, G. L Multivariate output analysis for Markov chain Monte Carlo, Biometrika, 106, 321-337.
multiESS, which calculates multivariate effective sample size using a
Markov chain and a function g.
ess which calculates univariate effective sample size using a Markov chain and a
function g.