Applied Statistics - Week 3
Monday the 4th - Friday the 8th of December 2017
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:
Particle Data Group (PDG) note on Monte Carlo.
Wiki transformation method.
Wiki Hit-and-Miss (Von Neumann) method.
Also, I'll be introducing the
problem set and
associated data on Tuesday (for noon Friday the 22nd of December).
Here is the associated
problem 4.1 data file
and
a Python script for reading it.
Here is the associated
problem 5.1 data file
and
a Python script for reading it.
Here is the associated
problem 5.2 data file
and
a Python script for reading it.
Monday:
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 a given distribution, and subsequently use
this.
Reading:
Glen Cowan: Chapter 3.
Lecture(s):
Monte Carlo methods.
Computer Exercise(s):
Making Random Numbers: MakingRandomNumbers.py
TransHitMiss: TransHitMiss.py
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.
Reading:
Barlow, chapter 5.3 to 5.7 (but not 5.5 and the proofs).
Lecture(s):
Likelihood function
I'll give an introduction to the problem set.
Computer Exercise(s):
Likelihood fit illustration: LikelihoodFit.py
ExampleLikelihoodFit.py: ExampleLikelihoodFit.py
which produces Fig_Background.png
and Fig_SignalBackground.png
TrackMinimizer.py: TrackMinimizer.py
which produces Fig_TrackMinuit.png
Friday:
I will do a summary of the curriculum discussed so far. This will also
give you an additional chance to ask questions about all exercises up
till now. For exercises, we will have some fun with a small little
exercise, illustrating the use of random numbers and simulation.
In the last part of the class, I will also introduce
the Project 2 data sets,
and start asking you about groups for these.
Reading:
Barlow, in which you should by now have read chapters 1-6!
Lecture(s):
Summary of curriculum so far.
Computer Exercise(s):
Pi Estimate: PiEstimate.py
Last updated: 3rd of December 2017.