I recently made a graph where I show the error bars for a certain number of "experiment". In another way, in my algorithm I'm minimizing the objective function so I would expect that increasing the sampling I'll get lower value of the objective function.
As you can see in the graph, the second value from the left, 2.5 on the x-axis, contain only 2.5% of the configurations, so we wouldn't expect it to perform as well as if we used 100% of the configurations.
I think that this is related to the asymmetry of the distributions. Is there any approach that can fix this problem - aka a method to compute CI for asymmetric unknown distributions?

This example should be useful to make this graph understandable!
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i = number of replicates (with different seed so different sampling every replicate)
z = objective function value
n = number of configurations
j = 1...n
Example: n=1000, i=100
- Step 1. Analyze all the
1000configurations and compute the minimum ofz_j. Store it and replicate fori. Then compute mu and sigma of thosez_i - Step 2. Analyze
50%of the initial1000configuration and compute the minimum ofz_j. Store it and replicate for i. Then compute mu and sigma of thosez_i - Step 3. Analyze
10%of the initial1000 - Step 4. Analyze
5%of the initial1000 - Step 5. Analyze
2.5%of the initial1000
So we will have mu_100, mu_50, mu_10, mu_5, mu_2.5 and mu_1 and sigma_100, sigma_50,...
Now I'm able to make those error bars like mu_100 + - 2 * sigma_100....