Compute a tail effective sample size estimate (tail-ESS) for a single variable. Tail-ESS is useful as a diagnostic for the sampling efficiency in the tails of the posterior. It is defined as the minimum of the effective sample sizes for 5% and 95% quantiles. For the bulk effective sample size see ess_bulk(). See Vehtari (2021) for an in-depth comparison of different effective sample size estimators.

ess_tail(x, ...)

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

# S3 method for rvar
ess_tail(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 (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

Aki Vehtari (2021). Comparison of MCMC effective sample size estimators. Retrieved from

See also


mu <- extract_variable_matrix(example_draws(), "mu")
#> [1] 322.0955

d <- as_draws_rvars(example_draws("multi_normal"))
#>          [,1]     [,2]     [,3]
#> [1,] 369.3083 238.6147 307.7817
#> [2,] 238.6147 363.2964 356.7673
#> [3,] 307.7817 356.7673 324.4500