Compute the basic effective sample size (ESS) estimate for a single variable
as described in Gelman et al. (2013) with some changes according to Vehtari et
al. (2021). For practical applications, we strongly
recommend the improved ESS convergence diagnostics implemented in
ess_tail(). See Vehtari (2021) for an in-depth
comparison of different effective sample size estimators.
ess_basic(x, ...) # S3 method for default ess_basic(x, split = TRUE, ...) # S3 method for rvar ess_basic(x, split = TRUE, ...)
(multiple options) One of:
A matrix of draws for a single variable (iterations x chains). See
Arguments passed to individual methods (if applicable).
(logical) Should the estimate be computed on split chains? The
If the input is an array, returns a single numeric value. If any of the draws
is non-finite, that is,
-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)
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.
Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari and Donald B. Rubin (2013). Bayesian Data Analysis, Third Edition. Chapman and Hall/CRC.
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
mu <- extract_variable_matrix(example_draws(), "mu") ess_basic(mu) #>  511.5225 d <- as_draws_rvars(example_draws("multi_normal")) ess_basic(d$Sigma) #> [,1] [,2] [,3] #> [1,] 680.2791 446.2236 481.9080 #> [2,] 446.2236 522.0755 418.0690 #> [3,] 481.9080 418.0690 636.2592