Applied Statistics - Week 2

Monday the 23rd - Friday the 27th of November 2020

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:
  • Friday of this week and Monday next week are special, as the class will be divided into two halves, which will alter between doing experiments for the project in First Lab, and follow the usual lectures and associated exercise (led by Nikki and Anna).
  • The exercise on Friday/Monday next week (i.e. 27th and 30th of November) is also a bit special, as this will the first time, that the exercise has little code in it! It is thus up to you to write/copy code into your analysis to yield the best estimate of the length of the table in Auditorium A along with an uncertainty.
  • Finally, the table measurement exercise is also slightly special in that we would like you to submit your answers, here: Table measurement submission form

    The project groups (Version 3.0, Tuesday the 26th of November) can be found here: ProjectGroups_v3.0_26nov.pdf.
    The overview of where to show up (and later do experiments) can be found here: AS2020_NBIoverview_ExperimentalLocations.pdf.



    Monday:
    Even in a complex world, a few PDFs play a central role again and again. We will go through these "natural" PDFs, in particular the Binomial, Poisson, and Gaussian distributions and see how they are related. Other PDFs will also be discussed. In the end, all of these PDFs are approximations to an idealised world - but they are a useful approximation!

    Reading:
  • Barlow, chapter 3
    Podcast:
  • Probability Density Functions.
    Lecture(s):
  • Probability Density Functions (Binomial, Poisson, and Gaussian)
    Zoom: Link to lecture.
  • Recording of Lecture video, Lecture audio, and Lecture chat.
    Computer Exercise(s):
  • Binomial, Poisson and Gaussian: BinomialPoissonGaussian_original.ipynb


    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 (and so the likelihood plays a central role in theoretical statistics). The exercise is more and illustration than a set of problems of what goes on behind the scene of fitting and the difference between a binned and an unbinned likelihood fit.

    Reading:
  • Barlow, chapter 5.1 to 5.7 (but not 5.5 and the proofs).
    Podcast:
  • Principle Of Maximum Likelihood.
    Lecture(s):
  • Maximum likelihood function
    Zoom: Link to lecture.
  • Recording of Lecture video, Lecture audio, and Lecture chat.
  • Recording of Lecture video and Lecture audio on the project.
    Computer Exercise(s):
  • Fitting Methods: FittingMethods_original.ipynb
  • Likelihood fit (partly for illustration): LikelihoodFit_original.ipynb

    Friday:
    Experiments for project: (Group A)
    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 13th of December 2020 (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 B)
    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
    Podcast:
  • Systematic Uncertainties.
    Lecture(s):
  • Systematic Errors
  • Systematic Errors (Pre-recorded Zoom lecture): Lecture video and Lecture audio.
    Computer Exercise(s):
    Zoom: Link to exercises.
  • Recording of Experiment Lecture video and Experiment Lecture audio.
  • 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


    The result of your table measurement analysis should be submitted here: Table measurement submission form, the purpose being an analysis of your results (without names!) showing to what extend you given the same data and the same questions can get different answers.

    In addition, the 2020 data exists in an expanded format, where the day of measurement was included: data_TableMeasurements2020_WithDates.txt
    If you managed to get a (good?) result on the "standard" problem, you can consider if the variations in the instructions for the measurements, affects the measurement results.
    Last updated: 22nd of November 2020.