Compute an effective sample size estimate for the standard deviation (SD) estimate of a single variable. This is defined as minimum of the effective sample size estimate for the mean and the the effective sample size estimate for the mean of the squared value.

ess_sd(x, ...)

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

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



(multiple options) One of:


Arguments passed to individual methods (if applicable).


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.


Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, and Paul-Christian Bürkner (2019). Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC. arXiv preprint arXiv:1903.08008.

See also

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


mu <- extract_variable_matrix(example_draws(), "mu") ess_sd(mu)
#> [1] 259.8527
d <- as_draws_rvars(example_draws("multi_normal")) ess_sd(d$Sigma)
#> [,1] [,2] [,3] #> [1,] 623.0794 382.0790 430.0359 #> [2,] 382.0790 512.1350 381.7729 #> [3,] 430.0359 381.7729 591.6446