Applied Statistics - Week 2

Monday the 27th of November - Friday the 1st 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:

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 (in Aud. A+B and around).

The exercise on Friday/Monday next week (i.e. 1st and 4th of December) 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 a minimal but realistic uncertainty.

The overview of where to show up (and later do experiments) can be found here: AS2023_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 (alternatively/better, Cowan, chapter 2)
Podcast:

Probability Density Functions.
Lecture(s):

Probability Density Functions (Binomial, Poisson, and Gaussian)

Recording of Lecture video I and Lecture video II (2022).
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 second exercise is more an illustration of what goes on behind the scene of fitting and the difference between a chisquare, 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

Trial Factors.

Recording of Lecture video (2022).
Computer Exercise(s):

Fitting Methods: FittingMethods_original.ipynb

Likelihood fit (exercise 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 (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.

Recording of Lecture video.
Computer Exercise(s):

Last updated: 22nd of November 2023.