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What is bootstrapping, and why is it a useful technique?

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Bootstrapping is a statistical method used to estimate the accuracy of a sample statistic by generating multiple samples from the original data with replacement. In other words, bootstrapping involves repeatedly resampling the data with replacement to create a large number of bootstrap samples, each of which is analyzed to obtain estimates of the population parameter of interest.

Here’s how bootstrapping works:

  • Data Preparation: The first step is to prepare the original data. The data can be any numerical data, such as the heights of individuals or the sales data of a company.
  • Sampling with Replacement: The second step is to generate multiple bootstrap samples by randomly selecting observations from the original data with replacement. Sampling data with replacement means that after any observation is sampled, the same observation can be sampled again at a later point in the process. This is different from sampling without replacement, where once an observation is drawn, it cannot be sampled again
Inforgraphic explaining the difference between sampling with replacement and sampling without replacement (Source: Data Sampling, Springer Link)
  • Estimation: After generating the bootstrap samples, the sample statistic of interest, such as the mean or the standard deviation, is calculated for each sample.
  • Analysis: The results of the bootstrap samples are then analyzed to obtain estimates of the population parameter of interest. This may involve calculating the mean or standard deviation of the bootstrap sample statistics or constructing a confidence interval.
Illustration of Bootstrapping process (Source: Bradley Boehmke website)

Advantages of Bootstrapping: Bootstrapping is useful when there are few observations in the original data set or it would be difficult to repeat the experiment on a separate sample of data. A sampling distribution can be created from a bootstrapped data set, where statistics such as the mean and quantiles can be estimated from the said distribution. One of the key advantages of Bootstrapping over traditional statistical methods is that it does not assume any specific distribution of the data, and it can be used with small sample sizes, which may not meet the assumptions of classical statistical methods. Bootstrapping is particularly useful in situations where the population parameter is unknown or difficult to estimate, or when the data is non-normal or skewed.

Bootstrapping technique is used in several machine learning algorithms such as Bagging, Random Forest and so forth.

A few commonly asked questions related to bootstrapping:

Q: Is the number of data sampled from bootstrap equal to original data?

A: Typically, the bootstrap samples are the same size as the original data set. This thread delves into the reasoning behind it.

Q: Why does bootstrapping require sampling with replacement (and not without replacement)?

A: If sampling is done without replacement, all the generated samples will be exactly the same and are going to have the same summary statistic as the original dataset providing no extra information

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