Compute the Monte Carlo standard error for the standard deviation (SD) of a single variable without assuming normality using moments of moments and first order Taylor series approximation (Kenney and Keeping, 1951, p. 141).

mcse_sd(x, ...)

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

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

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).

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

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

J. F. Kenney & E. S. Keeping (1951). Mathematics of Statistics, Vol. II.

Other diagnostics: ess_basic(), ess_bulk(), ess_quantile(), ess_sd(), ess_tail(), mcse_mean(), mcse_quantile(), pareto_diags(), pareto_khat(), rhat(), rhat_basic(), rhat_nested(), rstar()

Examples

mu <- extract_variable_matrix(example_draws(), "mu")
mcse_sd(mu)
#> [1] 0.2487345

d <- as_draws_rvars(example_draws("multi_normal"))
mcse_sd(d\$Sigma)
#>             [,1]       [,2]       [,3]
#> [1,] 0.007911205 0.01281948 0.01365999
#> [2,] 0.012819476 0.01966138 0.02375922
#> [3,] 0.013659991 0.02375922 0.04301713