Compute an effective sample size estimate for the standard deviation (SD) estimate of a single variable. This is defined as the effective sample size estimate for the absolute deviation from mean.

ess_sd(x, ...)

# S3 method for default
ess_sd(x, ...)

# S3 method for rvar
ess_sd(x, ...)

## Arguments

x

(multiple options) One of:

• A matrix of draws for a single variable (iterations x chains). See extract_variable_matrix().

• An rvar.

...

Arguments passed to individual methods (if applicable).

## Value

If the input is an array, returns a single numeric value. If any of the draws is non-finite, that is, NA, NaN, Inf, or -Inf, the returned output will be (numeric) NA. Also, if all draws within any of the chains of a variable are the same (constant), the returned output will be (numeric) NA

as well. The reason for the latter is that, for constant draws, we cannot distinguish between variables that are supposed to be constant (e.g., a diagonal element of a correlation matrix is always 1) or variables that just happened to be constant because of a failure of convergence or other problems in the sampling process.

If the input is an rvar, returns an array of the same dimensions as the rvar, where each element is equal to the value that would be returned by passing the draws array for that element of the rvar to this function.

## References

Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, and Paul-Christian Bürkner (2021). Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC (with discussion). Bayesian Data Analysis. 16(2), 667-–718. doi:10.1214/20-BA1221

Other diagnostics: ess_basic(), ess_bulk(), ess_quantile(), ess_tail(), mcse_mean(), mcse_quantile(), mcse_sd(), rhat_basic(), rhat(), rstar()

## Examples

mu <- extract_variable_matrix(example_draws(), "mu")
ess_sd(mu)
#> [1] 125.744

d <- as_draws_rvars(example_draws("multi_normal"))
ess_sd(d\$Sigma)
#>          [,1]     [,2]     [,3]
#> [1,] 219.9113 196.5978 256.7370
#> [2,] 196.5978 263.0422 213.1058
#> [3,] 256.7370 213.1058 273.2965