Applied Statistics - From data to results (Winter 2019-20)

"The art of drawing conclusions from experiments and observations consists in evaluating probabilities and in estimating whether they are sufficiently great or numerous enough to constitute proofs.
This kind of calculation is more complicated and more difficult than it is commonly thought to be."
[Antoine Lavoisier, French chemist 1743-1794]
Troels C. Petersen Etienne Bourbeau Sebastien G. Manigand Giulia Sinnl John Weaver Nikki Arendse
Lecturer - Associate Professor Teaching assistant - Ph.D. stud. Teaching assistant - Ph.D. stud. Teaching assistant - Ph.D. stud. Teaching assistant - Ph.D. stud. Teaching assistant - Ph.D. stud.
NBI - High Energy Physics NBI - High Energy Physics NBI - Astro- and Planetary Physics NBI - Ice and Climate NBI - Astronomy NBI - Cosmology
Mac user Windows & Linux expert Windows & Linux expert Windows expert Mac & Linux expert Mac expert
35 52 54 42 / 26 28 37 39 91 84 83 28 28 19 46 43 +39 340 989 1562 50 21 38 31 +31 637 448 001
petersennbi.dk etienne.bourbeauicecube.wisc.edu sebastiennbi.ku.dk giulia.sinnlnbi.ku.dk john.weavernbi.ku.dk nikki.arendsenbi.ku.dk


"Without data, you're just another person with an opinion." [William Edwards Deming, US statistician 1900-1993]

What, when, where, prerequisites, books, curriculum and evaluation:
Content: Graduate statistics course giving an advanced introduction to statistics and data analysis.
Level: Intended for students at 3rd-5th year of studies and new Ph.D. students.
Prerequisites: Math (calculus and linear algebra) and programming experience (any language, but see note below).
Note on prerequisites: Programming is an essential tool and necessary for the course!!!
When: Monday 8:15-12:00, Tuesday 13:15-17:00, and Friday 8:15-12:00 (Week Schedule Group B).
Note on morning lectures: After the first two weeks, we will start 9:15 on Mondays and Fridays.
Where: Lectures: Small UP1 (DIKU, Mon+Fri) and Auditorium 3 (HCO, Tues).
Exercises: A102+106+107 (Mon), 102+105+107 (Tues), and 103+104+107 (Fri) at HCO.
Period: Blok 2 (18th of November 2019 - 17th of January 2020), 7 weeks total (long Christmas vacation this year).
Format: Shorter lectures followed by computer exercises, discussion, and occationally experiments.
Text book: Roger Barlow: Statistics: A guide to the use of statistics.
Additional literature: Philip R. Bevington: Data Reduction and Error Analysis, Glen Cowan: Statistical Data Analysis.
Programs used: Simple Python (v3.6) and a few packages on top in Jupyter Notebook (see Nature article).
This has pro's but also con's, both of which are important to know about, e.g. Why I don't like notebooks!
For and introduction to ERDA and related issues, see the ERDA user guide.
Exercise/code repository: All code used for the exercises of the course can be found at AppliedStatisticsNBI GitHub.
Pensum/Curriculum: The course curriculum can be found here, which also contains a more detailed discussion.
Key words: PDFs, Uncertainties, Correlation, Chi-Square, Likelihood, Fitting, Monte Carlo and Data Analysis.
Expected learning: What I expect you to learn is discussed here: Learning objectives
Language: English (occational Danish utterings!). All exercises, problem sets, exams, notes, etc. are in English.
Evaluation: Problem set (20%), Project (20%), and take-home exam (60%).
Exam: Take-home (28 awake hours!) exam given Thursday the 16th of January 2020 at 8:00.
The exam will run from 8-24 on Thursday the 16th and again 6-18 on Friday the 17th of January (28 hours in total).
Censur: Internal censor evaluation (following the Danish 7-step scale)
Credits: 7.5 ECTS (1/8 academic years work, that is 187.5-225 hours of work, thus about 23-28 hours weekly).


Before course start:
Further course information can be found here: Applied Statistics course information.
The "course introduction" questionnaire to be filled out at: Applied Statistics 2019 Questionaire.
List of things to be done by first day of course (Monday the 18th of November): Applied Statistics check list.

Python specific precourse considerations:
The source of all code for this course is the NBI Applied Statistics github repository.
For a quick introduction to the basic git commands, please see the git cheat sheet.
Check your access to ERDA (requires KU ID), possibly following this guide.
NOTE: Many will always have tried ERDA, but for the right setup/packages, use "Statistics Notebook with Python".
Also, Install Python as described in README.md in version 3.6+, and put a few packages on top.
User Guides for the Minuit minimisation package: iminuit (2018). Perhaps, also see: Minuit Tutorial (2004).

"Essentially, all models are wrong, but some are useful". [George E. P. Box, British Statistician, 1919-2013]


Course outline:
Below is the preliminary course outline, subject to changes throughout the course.

Week 0: (Pre-course-start-session)
Nov 7: (15:15-17:00, Aud. A): Setting up Python, introduction, basic tips and trick to Python programming.
Nov 14: (10:15-12:00, Aud. A): More introduction, help, tips and trick to Python programming.

Problem set: (due Sunday 5th of January 2020 at 22:00)
     The problem set and the associated data files can be found here:
     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.


Week 1 (Introduction, General Concepts, ChiSquare Method):
Nov 18: 8:15-10:00 in Aud. A: Intro to course, photos, questionnaire, and table measurements.
     Central limit theorem. Mean, RMS and estimators. Correlation. Significant digits.
Nov 19: Error propagation (which is a science!). Estimate g measurement uncertainties.
Nov 22: ChiSquare method. Short Python Q+A (12-13). Formation of Project groups.

Week 2 (PDFs, Likelihood, Systematic Errors):
Nov 25: Probability Density Functions (PDF) especially Binomial, Poisson and Gaussian. Writing "Weighted mean" function.
Nov 26: Principle of maximum likelihood and fitting (which is an art!).
Nov 29: 8:15 - Group A: Project (for Sunday the 15th of December) doing experiments in First Lab.
              9:15 - Group B: Analysis of "Table Measurement data" and discussion of real data analysis (usual rooms).
             
Project Groups (version Tuesday 16:00): ProjectGroups.pdf.

Week 3 (Using Simulation, Likelihood, Fitting):
Dec 2: 8:15 - Group B: Project (for Sunday the 15th of December) doing experiments in First Lab.
            9:15 - Group A: Analysis of "Table Measurement data" and discussion of real data analysis (usual rooms).
Dec 3: Producing random numbers and their use in simulations.
Dec 6: Likelihood fits.

Week 4 (Hypothesis Testing and limits):
Dec 9: Hypothesis testing. Simple, Chi-Square, Kolmogorov, and runs tests.
Dec 10: Limits and confidence intervals. Testing random numbers.
Dec 13: Table Measurement solution discussion and Simpson's paradox.

Week 5 (Advanced Fitting and Calibration):
Dec 16: Advanced fitting and discussion of fitting strategies. Project should have been submitted! (along with residuals).
Dec 17: Calibration and use of control channels.
Dec 20: Evaluation of project results. Summary of curriculum so far. Session on Problem Set.

Week 6 (Bayes Theorem and Multivariate Analysis):
Jan 3: Bayes theorem. Multi-Variate Analysis (MVA). The linear Fisher discriminant.

Week 7 (Machine Learning and real data analysis):
Jan 6: Machine Learning (ML). Neural Networks, Decision Trees and other MLs. Problem set should have been submitted.
Jan 7: Analysis of real and complex data on separating/classifying events. Analysis of testbeam data (part I).
Jan 10: Problem set returned and discussed. Analysis of testbeam data (part II).

     For exam training, here is Exam2016.pdf, to be discussed shortly on Monday the 13th of January.
     Here is the associated problem 4.1 data file.
     Here is the associated problem 5.1 data file.
     Here is the associated problem 5.2 data file.
     Here is the solution manual for Exam2016.

Week 8 (Advanced fitting of real data and exam):
Jan 13: Advanced fitting. Short deliberation on previous exam.
Jan 14: Summary of course curriculum. Exam questions. Catch up on exercises.
Jan 16: Exam given (posted on course webpage 8:00 in the morning).
Jan 17: 18:00 Exam to be handed in (on www.eksamen.ku.dk).

Week 10? (Returning exam):
Jan 31: 15:15-16:30ish+ (Aud. ?): Exam solution, grades and course feedback.
     Designing experiments (inspired by "A lady tasting tea") with beer tasting? Or just beer...


"The best thing about being a statistician is that you get to play in everyone else's backyard." [John Tukey, Princeton University]




Notes and links:
In addition to the text book and other literature, some notes may be useful during the course:
  • PDG notes on Probability.
  • PDG notes on Statistics.
  • PDG notes on Monte Carlo Techniques.
  • Note on analytical fit of straight line.
  • Note on Frequentialist vs. Bayesian statistics and discoveries.
  • Note on rejecting data using Chauvenet's criteria.
  • Nature Physics article on discoveries.
  • Fisher's Exact Test on tea drinking lady.
  • Statistics resources.
  • Online course introducing Machine Learning..
  • Power Comparisons between tests of normality (spoiler alert: Shapiro-Wilk wins!)

    Course comments/praise (very biased selection!):
    "This course overqualified me for a course on scientific computing at Harvard the following Summer."
    [Dennis Christensen (2009 course), Venture Cup winner and now researcher at DTU Energy]

    "I recommended this course to everyone I know."
    [Pernille Yde (2009 course), now Head of Section of Data Science Lab at Statistics Denmark]

    "I don't think that you can rightly call yourself a physicist, if you have not had a course of this type."
    [Bo Frederiksen (2010 course)]

    "My second project in the course led to an article now in review for Nature magazine!" (it was accepted)
    [Ninna Rossen (2011 course)]

    "If you really want to understand your data, you need a course like this."
    [Julius Bier Kirkegaard (2012 course)]

    "I realized that I was very well prepared by this course, when I started working at CERN as a Summer Student."
    [Mathias Heltberg (2013 course)]

    "It is now many years ago, that I followed your course, but there is hardly a day, where I don't think about it"
    [Frederik Beyer (2011 course, in October 2014)]

    "This is without a doubt the single most useful, and possibly most influential, course I have taken during my university education. Thank you."
    [Samuel Walsh (2013 course, in December 2014)]

    "Tak for et fedt kursus. Naar jeg taenker tilbage paa mine 2.5 aars fysikstudier staar Anvendt Statistik frem som noget af det sjoveste og mest spaendende."
    [Martin Hayhurst Appel (2014 course)]

    "Every single sleepless night spent on this course has enriched my way of thinking."
    [Arianna Marchionne (2015 course)]

    "The best lecturer I had in my 3 years of studies in UCPH."
    [Anonymous (2016 course)]

    "I miss the course very much."
    [Niccolo Maffezzoli (instructor in 2015+2016 course, in 2017 as a PostDoc)]

    "I am able to confirm your course is very demanding but indeed worth working for, for I could spend another 7 weeks on this interesting curriculum!"
    [Jan de Boer 2017, upon having been told, that the course is demanding]

    "This course has been one of the most important aspects of my education so far. I have heard this from earlier students again and again - i am happy to say that i understand why now!"
    [Anonymous, Last line in the evaluation of 2017 course]

    "I learned a lot when I took the course, and still a good deal of things the year after, when I was a TA in the course."
    [Christian Michelsen, student in 2016 and TA in 2017+18 course]

    "Jeg gerne udtrykke min taknemmelighed for at have haft muligheden for at deltage i et saa velstruktureret og gennemfoert et kursus, som dit. Du burde vaere en inspiration for alle professorer paa universitetet".
    [From a student in the 2018 course, despite the person chosing the re-exam!]

    "I wanted to tell you, that this is the best course I ever had. And I've studied at four universities!"
    [Vlad-Andrei Neacsu (2018 course)]

    "Thank you for the amazing course. My view on measurements errors and statistics will never be the same."
    [Valdemaras Petrosius (2019 course)]

    "Thank you for the passing of knowledge. It was a mad statistical adventure, much more 'Applied' and worthwhile than any course I ever took!"
    [Che Fall (2019 course, writing from his native Canada after a non-optimal exam)]

    "Dear Troels. Thank you for an amazing course. Taking statistics to a level, where more than 100 students hang on your every word deserves more than just a pair of socks, but nonetheless, we hope that they will bring you as much joy as you have brought us."
    [Johann, Jonas, Jakob, and Chritian (2019 course, with a pair of socks!)]


    Last updated 21st of November 2019.