Statistical Data Analysis

6 EC

Semester 1, period 1

5354STDA6Y

Owner Master Physics and Astronomy (joint degree)
Coordinator dr. H.L. Snoek
Part of Master Astronomy and Astrophysics, track GRAPPA/Astro, year 1Master Physics and Astronomy, track GRAPPA, year 1

Course manual 2018/2019

Course content

This course intends to provide the statistical basis needed for the analysis of particle physics experiments. Both on the level of understanding the statistical concepts as on the level of computing needs.
This includes the following topics: Probability, Distributions of random variables, Examples of probability density functions, The Monte-Carlo method, Parameter estimation, The method of maximum likelihood, The method of least square, Testing the goodness-of-fit, Least square fitting with constraints.
Several exercises will be performed using the python programming language and the ROOT analysis framework. These include likelihood fits, pseudoexperiments and confidence limit setting.

Study materials

Syllabus

  • Statistical Data Analysis

Practical training material

  • Programming assignments in python/ROOT

Objectives

  1. Explain and apply the mathematical basis and foundations of probability and statistics.
  2. Demonstrate the propagation of (non-)correlated uncertainties.
  3. Explain the importance and limitations of random number generation.
  4. Design a simple simulation applying Monte Carlo techniques.
  5. Demonstrate the theory of maximum likelihood estimation and apply the approach to simplified problems.
  6. Apply and interpret the basics of hypothesis testing.
  7. Write and run procedural python programs using the ROOT framework and understand the basic concepts of object oriented programming.
  8. Apply statistical methods and analytical skills to a data analysis in a computer program.
  9. Interpret and effectively communicate, the results of a statistical data analysis in a short written report.
  10. Demonstrate problem-solving and critical thinking capabilities.

Teaching methods

  • Lecture
  • Computer lab session/practical training
  • Self-study

Lectures are given to introduce the topics to the students. A deeper understanding of the material will be achieved during self-study of the syllabus. The computer exercises provide hands-on application of the acquired knowledge. The results of the analyses in the exercises should be critically assessed and reported.

Learning activities

Activity

Number of hours

Hoorcollege

5

Tentamen

3

Werkcollege

51

Zelfstudie

109

Attendance

Requirements concerning attendance (OER-B).

  • In addition to, or instead of, classes in the form of lectures, the elements of the master’s examination programme often include a practical component as defined in article 1.2 of part A. The course catalogue contains information on the types of classes in each part of the programme. Attendance during practical components is mandatory.

    • Additional requirements for this course:

    Attendance during the scheduled course hours is required. In case of absence this has to be reported to the coordinator.

    Assessment

    Item and weight Details

    Final grade

    1 (50%)

    Tentamen

    		Must be ≥ 5.5

    1 (50%)

    Programming assignment

    		Must be ≥ 5.5

    1 (7%)

    A1

    2 (13%)

    A2

    2 (13%)

    A3

    3 (20%)

    A4

    3 (20%)

    A5

    4 (27%)

    A6

    The programming assignments have to be handed it according to the deadline schedule. Students need to contact the coordinator if they expect to miss a deadline.

    Inspection of assessed work

    Contact the course coordinator to make an appointment for inspection.

    Assignments

    A1 First analysis of a dataset

    • This assignment is intended to learn the student to work with the pyroot environment.

    A2 Error calculation

    • Put to practice the method of uncertainty propagation in the case of correlated and uncorrelated variables.

    A3 Large numbers and the central limit theorem

    • Learn to produce random numbers following distributions. Demonstrate the effects of the central limit theorem.

    A4 A shower of cosmic rays

    • Apply monte carlo techniques.

    A5 Maximum likelihood

    • Apply the method of maximum likelihood to a simplified analysis

    A6 Bump hunting

    • Demonstrate Hypothesis testing using maximum likelihood ratios on a simplified analysis.

    The assignments are computer exercises applying statistical data analysis techniques using pyroot. For all assignments a written report must be handed in by the student, together with the python code. Students work on the assignments individually. The assignments are assessed on the basis of code (operable, readable, optimal)  and  the report (clear description of method, good presentation of the results, interpretation and comparison of the results). Feedback will be given to the student during the practical hours. 

    Fraud and plagiarism

    The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

    Course structure

    Weeknummer Onderwerpen Studiestof Deadlines
    1 probability, random variables chapter 1,2,3  
    2 distributions, normal distribution, monte carlo methods chapter 4,5 A1, A2
    3 monte carlo methods   A3
    4 monte carlo methods    
    5 parameter estimation, maximum likelihood, hypothesis testing chapter 6,7 A4
    6 parameter estimation, maximum likelihood, hypothesis testing   A5
    7 parameter estimation, maximum likelihood, hypothesis testing   A6
    8      

    Timetable

    The schedule for this course is published on DataNose.

    Contact information

    Coordinator

    • dr. H.L. Snoek

    Staff

    • dr. A.J. Heijboer