Applied Statistics - Week 5

Monday the 18th - Friday the 22nd of December 2023

The following is a description of what we will go through during this week of the course. The chapter references and computer exercises are considered read, understood, and solved by the beginning of the following class, where I'll shortly go through the exercise solution.

General notes, links, and comments:
  • Lady tasting tea (Wikipedia).
  • Short note on Lady tasting tea.
  • How to produce (great?) plots: Plotting inspiration and code


    Monday:
    We will start the week by considering the theme MultiVariate Analysis (MVA), that is analysis of data with more than one (typically many) variables. To begin with, we will consider the relatively simple linear case, which is described by (Fisher's) Linear Discriminant Analysis (LDA), and then move on to more complex sets of data.
    Reading:
  • Barlow, chapter 7
  • An additional possible source is Fisher’s Linear Discriminant: Intuitively Explained
    Lecture(s):
  • Linear MultiVariate Analysis
    Computer Exercise(s):
  • 2par_discriminant.ipynb
  • fisher_discriminant.ipynb and Fisher's Iris data.

    Tuesday:
    The day will focus on calibration, which is a subtle subject, yet fairly straight forward, once you get the hang of the idea. The associated exercise is inspired by typical data analysis work.

    Reading:
  • No reading - logic and reason suffices.
    Lecture(s):
  • Calibration
    Computer Exercise(s):
  • Calibration: Calibration_original.ipynb (empty)
  • Calibration data file: data_calib.txt

    Friday:
    A central theme in probability and statistics is Bayes' Theorem, which concerns itself with prior probabilities, i.e. incorporating existing knowledge in evaluating outcomes. Many of you know this theorem already, but with this exercise we will try to bring a general perspective on data analysis along with it.
    In addition, we will have a look at Markov Chains and how they can be used in relation to Bayes' Theorem. Mathias will be giving the lecture and have designed the exercises.

    Reading:
  • Non - just listen in, ask questions, and wonder about these concepts.
  • NOTE: You should by now have read curriculum (roughly Barlow chapters 1-8).
    Lecture(s):
  • Bayes' theorem and Markov Chains
    Computer Exercise(s):
  • EhrenfestBallExperiment.ipynb.
  • DeterminingGenotypes.ipynb.
    Last updated: 13th of December 2023.