minESS: Minimum effective sample size required for stable estimation...
In mcmcse: Monte Carlo Standard Errors for MCMC

Description Usage Arguments Details Value References See Also Examples

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.

1	minESS(p, alpha = .05, eps = .05, ess = NULL)

`p`	dimension of the estimation problem.
`alpha`	Confidence level.
`eps`	Tolerance level. The eps value is ignored is `ess` is not `NULL`.
`ess`	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-α)\% confidence and tolerance of ε is

mESS ≥q \frac{2^{2/p} π}{(p Γ(p/2))^{2/p}} \frac{χ^{2}_{1-α,p}}{ε^{2}}.

The above equality can also be used to get ε from an already obtained estimate of mESS.

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.

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.