bootstrapping

The kind of operation where you use a thing to construct itself. Examples include using a compiler to compile a newer version of itself, using the core of an operating system to "boot" up the rest of the operating system.

In the case of the N Notation the notation itself is used to define its own structure. It does this by using a subset of its structures to allow the definition of more complex structures, which in turn are able to allow the definition of even more complex features and so on.

Another example is the language hierarchy that builds progressively more complex languages on the foundations of previous languages. Or not in the case of C# ;-)

Other terms: recursion, induction, ...

In statistical or mathematical terms, bootstrapping refers to a method of determining the behaviour of a model or a distribution through simulation. It is one of the Monte Carlo methods of simulation, along with permutation and jackknifing.

Using a real data series, bootstrapping allows a researcher to create a large number of hypothetical cases by resampling the data set with replacement. The fundamental procedure is as follows:

1. Identify the data series of interest. This data series will have n observations.
2. Calculate the parameter(s) of interest on the original data.
3. Select n random observations from the original data series, with replacement. This means that after selecting a case from the data, this case returns to the pool from which observations are randomly chosen. Thus, a single object may be selected more than once in any single simulation.
4. Calculate the parameter(s) of interest on this simulated data set.
5. Repeat steps 3-4 as many times as desired (normally many thousands of times).

This method of simulation has become increasingly appreciated and utilized in modern science. The reason for this is that it allows for the relaxation of many of the assumptions inherent in most theoretical distributions (such as the normal distribution, Poisson, Chi-squared, uniform etc.).