Applied Statistics - Week 3

Monday the 2nd - Friday the 6th of December 2019

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:


Monday:
Experiments for project: (Group B)
We will be working on the experiments for Project in First Lab.
This project should be handed in (PDF by mail to me) by 22:00 on Sunday the 15th of December 2019 (please, don't sit up all night!).
I would be very happy, if you would give the file the logical name "Project_GroupX_Name1Name2Name3Name4Name5.pdf", where NameX is the first name of the group members.

Lectures and exercises: (Group A)
Real data almost never follows theoretical PDFs, as the real world contains dirty wires, unknown biases, and mismeasurements. We will devote the day to discussion of real data analysis and systematic errors, and apply this to our "Table Measurements" from Aud. A.

Reading:
  • Barlow, chapter 4.4
  • Chauvenet's Criterion on Wikipedia
    Lecture(s):
  • Systematic Uncertainties (given by Etienne): Systematic Errors
    Computer Exercise(s):
  • TableMeasurements: TableMeasurement_original.ipynb,
    data_TableMeasurements2009.txt
    data_TableMeasurements2010.txt
    data_TableMeasurements2011.txt
    data_TableMeasurements2012.txt
    data_TableMeasurements2013.txt
    data_TableMeasurements2014.txt
    data_TableMeasurements2015.txt
    data_TableMeasurements2016.txt
    data_TableMeasurements2017.txt
    data_TableMeasurements2018.txt
    data_TableMeasurements2019.txt


    The result of your table measurement analysis should if possible be submitted in the Table measurement submission form by Thursday the 5th of December before 16:00 (after which I summarise the results).

    Tuesday:
    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 any given distribution, and subsequently use this.

    Reading:
  • Glen Cowan: Chapter 3.
  • Wiki transformation method.
  • Wiki Hit-and-Miss (Von Neumann) method.
  • Particle Data Group (PDG) note on Monte Carlo generators (optional - extends GC chapter 3).
    Lecture(s):
  • Monte Carlo methods.
  • Types of data and ways of plotting
    Computer Exercise(s):
  • Making Random Numbers according to any distribution:
             For illustration (with linear function): TransformationAcceptReject_simple_original.ipynb
             For testing (with 3rd degree polynomial): TransformationAcceptReject_pol3_original.ipynb
             For general problems (various functions): TransformationAcceptReject_general_original.ipynb
  • Estimating pi using uniform numbers: PiEstimate_original.ipynb


    Friday:
    The main theme will again be the Likelihood function, and how to use it when fitting data. This time the example is more advanced and a classic fitting case - some background with a possible Gaussian peak on it.
    In addition, I'll be lecturing on types of data and ways of plotting, and we'll shortly discuss Simpson's Paradox, which we jumped over a bit last week!

    Reading:
  • Barlow, chapter 5.3 to 5.7 (but not 5.5 and the proofs).
    Lecture(s):
  • Fitting peaks
  • Simpson's Paradox
    Computer Exercise(s):
  • Fitting peaks: FittingPeaks_original.ipynb
  • Fitting peaks ("Empty code" version): FittingPeaks_EmptyVersion_original.ipynb
    Last updated: 4th of December 2019.