Applied Statistics - Week 3
Monday the 4th - Friday the 8th 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:
The overview of where to show up (and later do experiments) can be found here:
AS2023_NBIoverview_ExperimentalLocations.pdf.
Monday:
Experiments for project: (Group A)
We will be working on the experiments for
Project in First Lab.
This project should be handed in (on Absalon) by 22:00 on Thursday the
14th of December 2023 (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 4.2.3 (short and very good!) and 4.4
Note on rejecting data using Chauvenet's criteria.
Optionally, Wikipedia also covers
Chauvenet's Criterion and
the more modern Peirce's Criterion.
Podcast:
Systematic Uncertainties.
Lecture(s):
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
data_TableMeasurements2020.txt
data_TableMeasurements2021.txt
data_TableMeasurements2022.txt
data_TableMeasurements2023.txt
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.
I'll also shortly comment on calculating a ChiSquare between two histograms and the Minuit
output.
Reading:
Interestingly, Barlow does not cover this important area, but there are fortunately plenty of other references:
Glen Cowan: Chapter 3 (highly recommended!).
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
Notes on binning
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 first morning lecture (for all) starting 9:15, so we will hopefully see you fresh and ready.
We will be working on fitting strategies when faced with real data and more complicated functions including discontinuities,
for which there is also an exercise (for those who want).
Finally, I'll be lecturing on types of data and ways of plotting, and we'll shortly discuss Simpson's Paradox.
Reading:
Barlow, chapter 5.3 to 5.7 (but not 5.5 and the proofs).
Lecture(s):
Fitting and significance
Minuit output explained
Notes on Normalisation in fits
Computer Exercise(s):
Fitting Danish Company Sizes:
CompanySizes_original.ipynb (empty version)
NBI Coffee Usage and Xmas vacation problem (discontinuous fitting):
CoffeeUsage_original.ipynb (empty version)
Weighted Mean - and relation to ChiSquare:
WeightedMeanSigmaChi2.ipynb (previously posted small exercise in preparation for project)
Last updated: 3rd of December 2023.