Description

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.

Usage

Arguments

Details

The minimum effective samples required when estimating a vector of length p, with 100(1-α)% confidence and tolerance of ε is

\mbox{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.

Value

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.

References

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).

See Also

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.

Examples