# Bootstraping as a technique for building confidence intervals

#statistic #statistics #statistical

20210114223129

When you want to extract a value from a series of data (like a `mean`

, a prediction from multiple weak classifiers - `RandomForests`

- etc.. ) you may also need to know a confidence interval for that number.

One analytical way of doing this is by employing a technique called Bootstrapping. This is a good whiteboard explanation for it.

The procedure is roughly the following:

- do multiple times (at least 10 000) the following:
- resample
*with replacement*a number of \(n\) elements from the original dataset (presumed to be of size \(n\) as well) - on the resulted series compute your desired metric

- resample
- at the end of the above loop you should have a series of metrics computed on a list of
*synthetic*(resampled) data akin to multiple Monte-Carlo simulations. - On the above series of metrics, compute the histogram as it should resemble a
*normal distribution*(bell shaped) - by the Law Of Large Numbers. - Compute the parameters of this normal distribution, the
*mean*and the*std*to see- where your confidence interval starts and end ( [-2
*std, +2*std] encompass 96.7% observations, [-3*std, 3*std] encompass 99.7% observations, etc..)

- where your confidence interval starts and end ( [-2

Find also here a refresher on confidence intervals computed directly on the *std* of a normal class

This video from Khan academy is also great at explaining p-value calculation

See also:

- https://www.khanacademy.org/math/statistics-probability/confidence-intervals-one-sample

## Backlinks

- Statistics course on Khan academy

- [[20210114223129]] Boostraping for confidence intervals

*Backlinks last generated 2022-01-08 20:08:39*

## Comments