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# Bootstrapping Method: Types, Working and Applications

• Soumyaa Rawat
• Jul 18, 2021

## What is the Bootstrapping Method?

A statistical concept, Bootstrapping is a resampling method used to stimulate samples out of a data set using the replacement technique. The process of bootstrapping allows one to infer data about the population, derive standard errors, and ensure that data is tested efficiently.

In simple terms, the Bootstrapping Method, in Statistics and Machine Learning, is a resampling statistical technique that evaluates statistics of a given population by testing a dataset by replacing the sample.

This technique involves repeatedly sampling a dataset with random replacement. A statistical test that falls under the category of resampling methods, this method ensures that the statistics evaluated are accurate and unbiased as much as possible.

Unlike other sampling distribution methods, the Bootstrapping method uses the samples procured from a study over and over again in order to use the replacement technique and ensure that the stimulated samples lead to an accurate evaluation.

Other than ensuring the sampling of the accuracy of a given dataset, bootstrapping in statistics also allows one to estimate the confidence intervals of a given dataset.

Bootstrapping Method, Source

A confidence interval is defined as the level of certainty with which an estimated statistic contains the true value of the parameter. Let us now discover more about the method.

In data science, information procured from a set of subjects is considered to be the building blocks of predictive patterns. Statistics and Machine Learning, in this sense, use past data to build predictive patterns for future use.

The bootstrapping method is highly significant in the field of statistics and has numerous applications. While the Jackknife resampling method and the Bootstrapping Method are two of the most common resampling methods, we will take a closer look at the Bootstrap method.

## Bootstrapping Method - How does it work?

Invented by Bradley Efron, the bootstrapping method is known to generate new samples or resamples out of the already existing samples in order to measure the accuracy of a sample statistic.

Using the replacement technique, the method creates new hypothetical samples that help in the testing of an estimated value.

Here are 3 quick steps that are involved in the Bootstrapping method -

1. Randomly choose a sample size.

2. Pick an observation from the training dataset in random order.

3. Combine this observation with the sample chosen earlier.

For the samples that are chosen in the representative sample size, they are referred to as the ‘Bootstrapped samples’ or the bootstrap sample size. On the other hand, the samples that are not chosen are referred to as the ‘Out-of-the-bag’ samples that serve as the testing dataset.

The bootstrapping method involves the bootstrapped samples or the training dataset being run through a machine learning model that is then tested using a new dataset - the Out-of-the-bag samples.

The purpose of the method is to enable the model to predict results for the out-of-the-bag samples, which normally lead to a normal distribution or a Gaussian distribution.

By using the replacement technique, the method follows the above-mentioned steps repeatedly (a minimum of 25 repetitions) in order to get better results.

It must be noted that the sample size chosen must be small and the process should be repeated multiple times in order to test the accuracy of the model in a better manner. Used to quantify the uncertain loopholes of a model, the bootstrapping method is an extremely insightful resampling procedure.

With respect to the specifics involved in the working of this method, there are 2 types of bootstrapping methods that are applicable in statistics and Machine Learning.

1. ### Parametric Bootstrap Method

In this method, the distribution parameter must be known. This means that the assumption of the kind of distribution the sample has must be provided beforehand.

For instance, it must be known to the user if the sample has Gaussian Distribution or Skewed distribution. This type of bootstrap method is more efficient since it already knows the nature of distribution.

Gaussian Distribution/ Normal Distribution

(Must catch: Statistical data distribution models)

1. ### Non-Parametric Bootstrap Method

Unlike the parametric bootstrap method, this type does not require the parameter of distribution to be known beforehand. Therefore, this type of bootstrap method works without assuming the nature of the sample distribution.

## Applications of the Bootstrapping Method

1. ### Hypothesis Testing

One of the best methods for hypothesis testing is the bootstrapping method. Unlike the traditional methods, the bootstrapping method allows one to evaluate the accuracy of a dataset using the replacement technique.

In the case of hypothesis testing in research, this method can be used to verify the accuracy of samples and a hypothesis can be proved to be valid or invalid.

All in all, bootstrap hypothesis testing mitigates the loopholes of a hypothetical model as opposed to the traditional method. When it comes to hypothesis testing, the bootstrapping method, unlike the traditional methods, does not anticipate that the data is normally distributed.

Thus, it is more accurate and better.

(Similar read: What is the p-value?)

1. ### Standard Error

The bootstrapping method is used  to efficiently determine the standard error of a dataset as it involves the replacement technique. The Standard Error (SE) of a statistical data set represents the estimated standard deviation.

SE represents the accuracy of a sample statistic and reflects the true statistical value of a sample in a given dataset.

While traditional methods are considered to be adequate to calculate standard error for a sample statistic, the bootstrapping method uses the replacement technique and ensures that more than one standard error value is calculated which collectively indicates the average SE.

This makes the method applicable in calculating standard error.

(Must Read - What is Standard Deviation?

1. ### Machine Learning

Unlike statistics, Bootstrapping in Machine Learning works quite differently. In the case of Machine Learning, the bootstrapping method accommodates the bootstrapped data for training Machine Learning Models and then tests the model using the leftover data points.

Machine Learning is on its way to evolving and has been advancing in every aspect possible. Using the replacement technique, ML models and algorithms  are tested using repeated sampling data points so as to ensure that they work accurately when it comes to independent data points.

Perhaps the application of Machine Learning is one of the biggest ones in the aspect of the bootstrapping method.

(Also read - Introduction to Machine Learning)

1. ### Bootstrapping Aggregation

Bagging in data mining, or Bootstrapping Aggregation, is an ensemble Machine Learning technique that accommodates the bootstrapping method and the aggregation technique.

While the bootstrapping method is a resampling procedure used to procure samples using the replacement technique, the technique of aggregation combines the predictive results obtained from multiple machine learning algorithms.

Instead of relying on one ML model, this ensemble technique of bootstrap aggregating focuses on gathering predictions from a number of models that lead to a more accurate and reliable prediction.

The bootstrapping method is applicable in this technique and has led to more efficient results in Machine Learning models.

1. ### Confidence Intervals

A Confidence Interval (CI) is a type of statistic that reflects the probability of a calculated interval containing a true value.

Using the bootstrapping method, samples are replaced with data points existing in a common dataset that leads to more accurate and efficient results related to CI.

While estimating samples, the confidence interval tells us how true an estimated sample value is with respect to the other samples collected.

Lastly, the bootstrapping method is known to test the accuracy of statistics like the confidence interval that helps one to verify the accuracy of a sample statistic altogether.

## Pros & Cons of the Bootstrapping Method

Pros of the bootstrapping method are following;

1. ### Functionally Simpler

The bootstrapping method is a functionally simpler way to estimate the value of statistics that are otherwise too complicated to calculate using the traditional methods.

A straightforward way, the method allows for easier checks and simpler steps to process the accuracy of a model, without much hassle.

1. ### Accurate Results

The bootstrapping method, one of the most renowned resampling methods, does not require any pre-assumptions for its concept to work.

Unlike traditional methods that rely on the theoretical concept to produce results, the bootstrapping method simply observes the results and works on them, producing accurate results.

The method does not fail even when the theory does not support the practical observations, and is thus, very advantageous in this aspect.

(Read also: Types of Sampling Techniques)

Listing below some cons of bootstrapping method;

1. ### Excessive Computing Power

Using the replacement technique, the bootstrapping method resamples data points in order to accurately test a model’s performance.

In this case, the method requires excessive computing power since it is supported by the replacement technique. One of the disadvantages of the bootstrapping method, the excessive computing power can weigh down its benefits.

1. ### Underestimates the Variability

As the bootstrapping method is recommended to work effectively in the case of small sample sizes, one of the drawbacks of this method is that it is prone to underestimate the variability of the distribution.

In the case of rare-extreme values, the method tends to largely accommodate closer values, avoiding the participation of near-end values.

(Suggested blog: What is Sampling Distribution?)

## In the End

In the end, the bootstrapping method is an extremely insightful method of testing the accuracy of a model when the theoretical distribution of its samples is unknown.

By segregating the dataset into bootstrap samples and out-of-the-bag samples, the method involves a simpler approach to calculate multiple statistics like the confidence intervals, standard error, and even determining potential drawbacks of an ML model.

Even though the method can underestimate the variability of data and requires excessive computing power, it is known to produce better and accurate results with the help of the replacement technique.