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I'm reading a paper and am confused with their described Bootstrap Method. the text says:

the uncertainties associated with each stacked flux density are obtained via the bootstrap method, during which random subsamples (with replacement) of sources are chosen and re-stacked. The number of sources in each subsample is equal to the original number of sources in the stack. This process is repeated 10000 times in order to determine the representative spread in the properties of the population being stacked.

So, say I have 50 values. I find the average of these values. According to this method, I would get a subsample from this original 50 population and find that average, and repeat this 10,000 times. Now, how would I get a subsample "equal to the original number of sources in the stack" without my subsample BEING EXACTLY THE SAME AS THE ORIGINAL, AND THUS THE EXACT SAME MEAN, WHICH WOULD TELL US NOTHING!?

idmean
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user3727154
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  • Because your subsample isn't going to be exactly the same as you draw with replacement. So if you repeat it 10000 times you will end up with the mean of some subsamples being considerably lower and other higher because you will draw a disproportionally amount of low and high values respectively. – horseoftheyear Jun 17 '14 at 13:21
  • but i have no values to replace it with - I only have those 50 values – user3727154 Jun 17 '14 at 16:52
  • can you explain with an example maybe? – user3727154 Jun 17 '14 at 16:52
  • "but i have no values to replace it with - I only have those 50 values" -- sampling with replacement means that you take a datum at random, then figuratively "put it back", then take another datum. Since you "put it back", it could be chosen again. With a finite number of data, some of the data will be chosen more than once, and conversely some will not be chosen at all; that makes the sample mean different from one bootstrap sample to another. – Robert Dodier Jun 17 '14 at 20:11
  • Above is a good explanation. If you want to know a bit more about the technical aspects [this article](https://www.americanscientist.org/issues/pub/2010/3/the-bootstrap) might be useful. – horseoftheyear Jun 18 '14 at 11:23
  • thanks everyone - I talked to a stats friend the other day and figured it out – user3727154 Jun 18 '14 at 12:53

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you can reuse values. So if i have ABCDE as my values, i can bootstrap with AABCD, etc. I can use values twice, that is the key

user3727154
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