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)
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
.
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
.
The minimum effective samples required when estimating a vector of length p, with 100(1-\(\alpha\))% confidence and tolerance of \(\epsilon\) is
$$\mbox{mESS} \geq \frac{2^{2/p} \pi}{(p \Gamma(p/2))^{2/p}} \frac{\chi^2_{1-\alpha, p}}{\epsilon^2} $$
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 (to appear).
Vats, D., Flegal, J. M., and, Jones, G. L Multivariate Output Analysis for Markov chain Monte Carlo, arXiv preprint arXiv:1512.07713 (2015).
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.