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:
A matrix of draws for a single variable (iterations x chains). See
extract_variable_matrix().
An rvar.
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 https://avehtari.github.io/rhat_ess/ess_comparison.html
Other diagnostics:
ess_basic(),
ess_bulk(),
ess_quantile(),
ess_sd(),
mcse_mean(),
mcse_quantile(),
mcse_sd(),
pareto_diags(),
pareto_khat(),
rhat(),
rhat_basic(),
rhat_nested(),
rstar()
mu <- extract_variable_matrix(example_draws(), "mu")
ess_tail(mu)
#> [1] 322.0955
d <- as_draws_rvars(example_draws("multi_normal"))
ess_tail(d$Sigma)
#> [,1] [,2] [,3]
#> [1,] 369.3083 238.6147 307.7817
#> [2,] 238.6147 363.2964 356.7673
#> [3,] 307.7817 356.7673 324.4500