minESS {mcmcse}

Minimum effective sample size required for stable estimation as described in Vats et al. (2015)

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

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

Arguments

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.

Details

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.

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, 25, 684–-700.

Vats, D., Flegal, J. M., and, Jones, G. L Multivariate output analysis for Markov chain Monte Carlo, Biometrika, 106, 321–-337.

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

minESS(p = 5)