Applied Statistics - Week 3

Monday the 6th - Friday the 10th of December 2021

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:
The overview of where to show up (and later do experiments) can be found here: AS2021_NBIoverview_ExperimentalLocations.pdf.

Monday:
Experiments for project: (Group B)
We will be working on the experiments for Project in First Lab.
This project should be handed in (on Absalon) by 22:00 on Wednesday the 15th of December 2021 (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
  • Peirce's Criterion on Wikipedia
    Podcast:
  • Systematic Uncertainties.
    Lecture(s):
  • Systematic Errors.
    Zoom: Link to lecture.
                  Link to exercises.
    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
    data_TableMeasurements2020.txt
    data_TableMeasurements2021.txt

    The result of your table measurement analysis should be submitted in the Table measurement submission form, by Thursday the 9th of December before 11:00 (after which we summarise the results). The purpose is to show your analysis results (without names, so don't worry!), seeing to what extend you - given the same data and the same questions - can get different answers.


    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:
    Interestingly, Barlow does not cover this important area, but there are fortunately plenty of other references:
  • Glen Cowan: Chapter 3.
  • Wiki on transformation method.
  • Wiki on rejection sampling (Von Neumann) method.
  • Particle Data Group (PDG) note on Monte Carlo generators (optional - extends Cowan's chapter 3).
    Lecture(s):
  • Monte Carlo methods.
  • ChiSquare between histograms
    Zoom: Link to lecture.
                  Link to exercises.
    Computer Exercise(s):
  • Making Random Numbers according to any distribution:          For your illustration (with linear function): TransformationAcceptReject_simple.ipynb
             For your testing (with 3rd degree polynomial): TransformationAcceptReject_pol3.ipynb
             For your exercise (various functions): TransformationAcceptReject_general.ipynb


    Friday:
    This Friday will be the last morning lecture (for all) starting 8:15, and it will fall into two parts. The first part will be a summary of curriculum until now, where I will re-iterate on subjects, and answer questions about them. The second part will be on fitting strategies when faced with real data and more complicated functions including discontinuities.
    I'll also shortly comment on calculating a ChiSquare between two histograms and the Minuit output. Finally, I'll be lecturing on types of data and ways of plotting, and we'll shortly discuss Simpson's Paradox, for which there is also an exercise (for those who want).

    Reading:
  • Barlow, chapter 5.3 to 5.7 (but not 5.5 and the proofs).
    Lecture(s):
  • Minuit output explained
  • Fitting and significance
  • Types of data and ways of plotting
  • Simpson's Paradox
    Zoom: Link to lecture.
                  Link to exercises.
    Computer Exercise(s):
  • Fitting Danish Company Sizes: CompanySizes_original.ipynb
  • NBI Coffee Usage and Xmas vacation problem (extra problem): CoffeeUsage_original.ipynb (empty version)
  • Weighted Mean - and relation to ChiSquare: WeightedMeanSigmaChi2.ipynb (previously posted small exercise in preparation for project)
    Last updated: 1st of December 2021.