In statistics, especially inferential statistics, the corner stone paradigm is that of sample-population.
We most often don’t have the population details. We hence try to infer things about the population through the sample.
For e.g. Population parameter is estimated through sample statistic.
โช What is Bootstrapping?
Bootstrapping simply put is a method of repeated sampling (with replacement) of a sample. The sample chosen is assumed to be a good representation of the population.
โช What is the utility of Bootstrapping?
Bootstrapping should be seen as a method to learn about the sampling distribution rather than a method to estimate the population parameter.
If we take simple linear regression as example, the model is fit to data and is used to make inferences about a larger population, hence the implicit assumption in interpreting regression coefficients is that the sample is representative of the population.
The question then arises about the quality of the sample and its estimate.
How can we be sure of the coefficients in linear regression? Bootstrapping can provide information about the variability of the coefficients.
Bootstrapping can hence be used to construct confidence intervals.
โช Communality between Bootstrapping and Confidence Intervals
One communality between bootstrapping and confidence intervals is ‘repeated sampling’.
Many get the explanation of the confidence interval wrong because they forget the ‘repeated sampling’ that is inherent in the process of constructing CI.
๐ How we use Bootstrapping in MMM.
MMM is built using various forms of Multi linear regression.
The core emphasis is on attribution. This attribution is made possible because of the coefficients. Therefore it becomes imperative that we are really sure about coefficients, because many of the downstream applications like saturation curves, budget optimization etc. are artifacts of the MMM model.
Bootstrapping thus helps us by providing information about coefficient variability.
Overall, bootstrapping helps us build robust MMM models. And robust MMM models are the models which clients can trust.
P.S: There is huge body of work wrt to bootstrapping. One excellent resource is the “An introduction to the bootstrap” by Bradley Efron and Rob Tibshirani.
Resource:
Clearing Misconceptions around Confidence Interval. โ https://bit.ly/3HgOOIn
