Applied Statistics - Week 2

Monday the 26th - Friday the 30th of November 2018

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 (done by Etienne and Sebastien).

The exercise on Friday/Monday next week (i.e. 29th of November and 2nd 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.

Finally, the table measurement exercise is also slightly special in that we would like you to submit your answers, here: Table measurement submission form

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
Lecture(s):

Binomial, Poisson, and Gaussian
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).
Lecture(s):

Maximum likelihood function
Computer Exercise(s):

Likelihood fit 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 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 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
Lecture(s):

Systematic Uncertainties (given by Christian "Hævi" Michelsen): Systematic Errors
Computer Exercise(s):

Last updated: 21st of November 2019.