Squared error of the mean calculated as
$$ \textrm{mean}(\textrm{observed} - \textrm{mean prediction})^2 $$ The mean prediction is calculated as the mean of the predictive samples.
Examples
observed <- rnorm(30, mean = 1:30)
predicted_values <- matrix(rnorm(30, mean = 1:30))
se_mean_sample(observed, predicted_values)
#> [1] 0.014829896 0.316608439 1.142566519 0.086187944 0.058926355
#> [6] 3.073734463 0.002511154 0.008577179 3.999907031 1.048431205
#> [11] 0.281251491 2.816708187 12.593948837 1.990408824 0.123815451
#> [16] 0.569334753 1.956832571 0.052113786 1.198119654 0.285800371
#> [21] 0.113974757 8.105728298 0.019562959 0.737141759 0.375735782
#> [26] 0.062009545 0.058334996 0.492055176 0.007062469 0.978271085