Illustration of sampling variance of a random sample of size 100, of two unit variance zero mean normal distributed parameters:
The corresponding deterministic sampling of the population, inferred from 10 000 sets of random samples of size 100 (as in the illustration above covering only 100 sets):
The most general sampling method, or Sampler is provided by the random Annealer framework, here sampling one parameter with 5 samples to represent the statistical moments 1-4 (accurately) and 5-8 (approx), of its given continuous uniform distribution:
This exemplifies our concept SavvySampler®, dedicated to efficient consistent sampling of models, emphasizing deterministic sampling but also encompassing various odd flavors of random sampling, like Latin Hypercube Re-sampling. It illustrates sampling variance of co-variance, a hardly known but nevertheless often the dominant contributions to the random error of random sampling (RS). RS is widely utilized as a simple method to quantify the uncertainty of models. Another example is the evaluation of uncertainty of random sampling, i.e. the uncertainty of the evaluated uncertainty. That is what the red points illustrate in the figure above.
SavvySampler® methodology is currently practiced in applications of nuclear power, meteorology and by ourselves in road quality evaluation (RoadNotes®).
[Contact us for more information.]