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 $$mESS \geq \frac{2^{2/p} \pi}{(p
\Gamma(p/2))^{2/p}} \frac{\chi^{2}_{1-\alpha,p}}{\epsilon^{2}}.$$
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<U+2013>-700.
Vats, D., Flegal, J. M., and, Jones, G. L Multivariate output analysis for Markov chain Monte Carlo, Biometrika, 106, 321<U+2013>-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.