7. The Bootstrap#

This week we will be thinking about random variability across samples

Often, we have a relatively small sample of data, and want to infer from it something about the properties of a parent or population distribution. For example I measure the heights of 10 men and calculate the mean - this gives me an estimate of the mean height of all men, but how much would my estimate change if I had randomly selected 10 different men for my sample?

Last week we started by looking at the unusual case in which the population or parent distribution is available to us. We will simulated the process of drawing many samples of size n from a parent distribution, and taking the mean of each sample. The distribution of these means, known as the sampling distribution of the mean, describes the expected random variability in the mean for different samples.

We also saw that for certain situations the sampling distribution of the mean can be predicted from theory - we saw that the sammpling distribution can sometimes be modelled as a normal distribution (for large samples) or a t distribution (for normal data)

This week we will meet an empirical (sampling based) technique to establish the sampling distribution of and statsitic, for any sample size, for any data distribution.

Meet the bootstrap!

7.1. Tasks for this week#

Conceptual material is covered in the lecture. In addition to the live lecture, you can find lecture videos on Canvas.

Please work through the guided exercises in this section (everything except the page labelled “Tutorial Exercises”) in advance of the computer-based tutorial session.

To complete the guided exercises you will need to either:

  • open the pages in Google Colab (simply click the Colab button on each page), or
  • download them as Jupyter Notbooks to your own computer and work with them locally (eg in Spyder)

If you find something difficult or have questions, you can discuss with your tutor in the computer-based tutoral session.

This week is particularly heavy on conceptual material, so please do discuss the guided exercises and tutorial exercises with your tutor to make sure you understand