Note that there are some duplicates since a bootstrap resample comes from sampling with replacement from the data.
2.
In statistics, "'bootstrapping "'is any test or metric that relies on random sampling with replacement.
3.
Since we are sampling with replacement, we are likely to get one element repeated, and thus every unique element be used for each resampling.
4.
From this perspective, the case labeled " Surjective " f " " is somewhat strange : Essentially, we keep sampling with replacement until we've chosen each item at least once.
5.
In the terminology below, the case of sampling with replacement is termed " Any " f " ", while the case of sampling without replacement is termed " Injective " f " ".
6.
This is vaguely comparable to the coupon collector's problem, where the process involves " collecting " ( by sampling with replacement ) a set of " X " coupons until each coupon has been seen at least once.
7.
In order to reason about the population, we need some sense of the sampling with replacement so, assuming N is sufficiently large, for all practical purposes there is virtually zero probability that it will be identical to the original " real " sample.
8.
Note however that you can never explicitly " determine " the number of different words in the bag by sampling with replacement, but you can " estimate " it with decent precision . talk ) 18 : 31, 1 August 2014 ( UTC)
9.
Because of the simple " sampling with replacement " scheme in this second case, the urn content is now " static ", but this greater simplicity is compensated for by the assumption that the urn content is now " unknown " to an observer.
10.
In both of these models, the act of measurement has an effect on the outcome of future measurements . ( For comparison, when sampling with replacement, observation of a particular value has no effect on how likely it is to observe that value again . ) Note also that in a P�lya urn model, successive acts of measurement over time have less and less effect on future measurements, whereas in sampling without replacement, the opposite is true : After a certain number of measurements of a particular value, that value will never be seen again.
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