A Practical Guide to Bootstrap with R Examples

A Practical Guide to Bootstrap with R Examples

Bootstrap is a resampling method where large numbers of samples of the same size are repeatedly drawn, with replacement, from a single original sample.

TLDR

  • Bootstrap is a resampling method with replacement.
  • It allows us to estimate the distribution of the population.
  • In Machine Learning, bootstrap estimates the prediction performance while applying to unobserved data.
  • R illustrations

What is bootstrap?

Bootstrap is a resampling method where large numbers of samples of the same size are repeatedly drawn, with replacement, from a single original sample. It attempts to gauge the distribution of the population even with one finite sample. The beauty of bootstrapping is that it creates resulting samples following a Gaussian distribution, making a lot of statistical inference possible.

It has the following steps:

  1. decide how many bootstrap samples to perform
  2. what is the sample size
  3. for each bootstrap sample:
  • draw a sample with replacement with the chosen size
  • calculate the statistic of interest for that sample

4. calculate the mean of the calculated sample statistics

Fortunately, we don’t have to manually do the calculations, and R has a package, boot, that handles the hard work for us (more information on the R illustration section).

Why bootstrap?

Before answering why bootstrap, let’s dig into some common challenges that we face while drawing statistical inference.

  • After A/B tests, to what extent can we trust a small sample size (say, 100) would represent the true population?
  • If sample repeatedly, will the estimate of interest vary? If they do vary, what does the distribution look like?
  • Is it possible to make valid inferences when the distribution of the population is too complicated or unknown?

As data scientists, we are tasked to make inferences about the population distribution all the time, as the above scenario shows. However, any valid inference process requires strict statistical assumptions, which may not hold or remain unknown. Ideally, we would like to survey the entire population and ask for answers. This approach is way too expensive and time-consuming. It is impossible to ask every American who they would vote for in the upcoming Presidential election if we are interested in political prediction.

To draw inference, we sample a portion of the population, say 10K Americans, and ask for their picks. This approach is less expensive and more practical to implement. However, it does not come without challenges. We may get slightly different results every single time we draw a sample. In other words, the standard deviation of a point estimate could be considerably large for repeated samplings, which may bias the estimator.

As a non-parametric estimation method, bootstrap comes in handy and quantifies the uncertainty of an estimator involved with the standard deviation.

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