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_bulk() and 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, ...)

## 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).

split

(logical) Should the estimate be computed on split chains? The default is TRUE.

## 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

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

## See also

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

## Examples

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