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 |

`p` |
dimension of the estimation problem. |

`alpha` |
Confidence level. |

`eps` |
Tolerance level. The eps value is ignored is |

`ess` |
Estimated effective sample size. Usually the output value from |

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.

1 | ```
minESS(p = 5)
``` |

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