Applied Statistics - Week 3

Monday the 4th - Friday the 8th of December 2017

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:
  • Particle Data Group (PDG) note on Monte Carlo.
  • Wiki transformation method.
  • Wiki Hit-and-Miss (Von Neumann) method.

    Also, I'll be introducing the problem set and associated data on Tuesday (for noon Friday the 22nd of December).
    Here is the associated problem 4.1 data file and a Python script for reading it.
    Here is the associated problem 5.1 data file and a Python script for reading it.
    Here is the associated problem 5.2 data file and a Python script for reading it.

    Monday:
    We will consider Monte Carlo Techniques, which is a ubiquitious tool in statistics. The central point is to be able to generate random numbers according to a given distribution, and subsequently use this.

    Reading:
  • Glen Cowan: Chapter 3.
    Lecture(s):
  • Monte Carlo methods.
    Computer Exercise(s):
  • Making Random Numbers: MakingRandomNumbers.py
  • TransHitMiss: TransHitMiss.py

    Tuesday:
    The main theme will be the Likelihood function, and the central role it plays in statistics. It is in principle the most powerful method for fitting, and estimation and ChiSquare can be derived from it.

    Reading:
  • Barlow, chapter 5.3 to 5.7 (but not 5.5 and the proofs).
    Lecture(s):
  • Likelihood function
    I'll give an introduction to the problem set.
    Computer Exercise(s):
  • Likelihood fit illustration: LikelihoodFit.py
  • ExampleLikelihoodFit.py: ExampleLikelihoodFit.py which produces Fig_Background.png and Fig_SignalBackground.png
  • TrackMinimizer.py: TrackMinimizer.py which produces Fig_TrackMinuit.png

    Friday:
    I will do a summary of the curriculum discussed so far. This will also give you an additional chance to ask questions about all exercises up till now. For exercises, we will have some fun with a small little exercise, illustrating the use of random numbers and simulation. In the last part of the class, I will also introduce the Project 2 data sets, and start asking you about groups for these.

    Reading:
  • Barlow, in which you should by now have read chapters 1-6!
    Lecture(s):
  • Summary of curriculum so far.
    Computer Exercise(s):
  • Pi Estimate: PiEstimate.py
    Last updated: 3rd of December 2017.