The problem with straight bootstrapping
What you could see happening was that with a single observation of data, bootstrapping will give the same answer every time. Ironically, this means that when you're bootstrapping such a small dataset, you will have zero variance. Here's an example in code:
plt.hist([np.random.choice([1]) for i in range(100)])
The histogram for sampling from a dataset that consists of only one element looks as follows:
As predicted, every value is the same. This doesn't really match our intuition about uncertainty though. We have only observed a single number, but it could have just as easily been a different number. This technique ...
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