Applied Statistics - From data to results (Winter 2016-17)

The final take-home exam has been posted!
Hand in (petersennbi.dk) by Friday 20th of January 2017 at 12:00.
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.


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 below).
	Note on prerequisites: Programming is an essential tool and necessary for the course!!!
When:	Monday 9-12, Tuesday 13-17, and Friday 9-12 (Week Schedule Group B).
Where:	Lectures: Auditorium A, Exercises: Auditorium M (and around there) at NBI.
Period:	Blok 2 (21st of November 2016 - 20th of January 2017), 7.3 weeks total (missing two Fridays).
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 (v2.7) and the CERN software ROOT (v5.34).
Pensum/Curriculum:	The course curriculum can be found here.
Key words:	PDFs, Uncertainties, Correlation, Chi-Square, Likelihood, Fitting, Monte Carlo and Data Analysis.
Language:	English (occational Danish utterings!). All exercises, problem sets, exams, notes, etc. are in English.
Evaluation:	Problem set (15%), two projects (25%), and take-home exam (60%).
Exam:	Take-home (28 hour) exam given Thursday the 19th of January 2017 at 8:15.
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 23-28 hours weekly).

Before course start:
Further course information can be found here: Applied Statistics course information
Expected learning objectives of the course are discussed here: Learning objectives
A "course introduction" questionnaire can be found at: Applied Statistics 2016 Questionaire
List of things to be done by first day of course (Monday the 21st of November): Applied Statistics check list


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

Week 0: (Pre-course-start-session)
Nov 16: (10:15-12:00): Setting up computers, Installation of Python and ROOT (Aud. M).
Nov 17: (10:15-12:00): Introduction, tips and trick to Python/ROOT programming (Aud. M).

Introduction to Python (also read more here: Dive into Python): PythonIntro.py

Introduction to ROOT (also read more here: ROOT examples): RootIntro.py

Producing nice plots: nicefig.py, which produces this figure.

Week 1 (Introduction, general concepts)
Nov 21: 8:15: Intro to course, photos, questionnaire and table measurements (Aud. A).
     Central limit theorem. Mean, RMS and estimators. Correlation. Significant digits.
Nov 22: Error propagation (which is a science!) and short Python+ROOT tutorial.
Nov 25: ChiSquare method (which plays a central role in the course!).
     Form Project 1 groups. Estimate g measurement uncertainties.

Week 2 (ChiSquare, Systematic Errors)
Nov 28: 8:15: Start project 1 (for Thursday the 8th of December) doing experiments in First Lab.
Nov 29: Probability Density Functions (PDF) especially Binomial, Poisson and Gaussian.
Dec 2: Analysis of "Table Measurement data" and discussion of real data analysis.

Week 3 (Likelihood, Fitting, Using Simulation):
Dec 5: 8:15 Producing random numbers and their use in simulations.
Dec 6: Principle of maximum likelihood and (more) fitting/examples.
Dec 9: Simulation exercises and summary (having handed in project 1 and residuals).
     Handing out problem set and data (for noon Friday the 23rd of December).
     Problem 4.1: data file and script, Problem 4.2: data file and script.

Week 4 (Hypothesis Testing and limits):
Dec 12: Hypothesis testing. Simple, Chi-Square, Kolmogorov and runs tests.
Dec 13: Limits and confidence intervals.
Dec 16: Calibration and use of control channels. Table measurement solution.

Week 5 (Bayes Theorem and classification):
Dec 19: Bayes theorem and separating/classifying events. Analysis of testbeam data (part I). Evaluation of project 1 results.
Dec 20: Analysis of testbeam data (part II). Session on Problem Set.
Dec 23: Vacation - no teaching! Only requirement is an accepted Project 2 (for Sunday the 15th of January).

Week 6 (Multivariate Analysis):
Jan 2: More on hypothesis testing and Project 2 status.
Jan 3: Multi-Variate Analysis (MVA) part I. The linear Fisher discriminant.
Jan 6: Multi-Variate Analysis (MVA) part II. Neural Networks, Decision Trees and other MVAs.
     Returning and discussing problem set
     For exam training, posting Exam2011.pdf

Week 7: (Advanced fitting and project 2)
Jan 9: Advanced fitting and Project 2 work.
Jan 10: More advanced fitting and Project 2 work. Possibly introduce Weights and sWeights.
Jan 13: Planning of an experiment and Project 2 work. (Hand in Project 2 by Sunday 15th, 22:00).

Week 8 (Project 2 presentations and exam):
Jan 16: Project 2 presentations. Short deliberation on 2011 exam.
Jan 17: Project 2 presentations. Summary/repetition of course curriculum.
Jan 19: Exam given (posted on course webpage 8:15 in the morning).
Jan 20: 12:00 Exam to be handed in (by Email to Troels Petersen).

Week 9 (Returning exam):
Jan 27: 13:15-14:30ish+ (Aud. M): Exam solution, grades and course feedback.
     Designing experiments (inspired by "A lady tasting tea") with beer tasting?




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..

Links:

Blog on how to use crime rates for predicting taxi demand!.

Comments about course (biased selection!):

"This course overqualified me for a course on scientific computing at Harvard the following Summer." [Dennis Christensen (2009 course)] "I recommended this course to everyone I know." [Pernille Yde (2009 course)] "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!" [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)]

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Last updated 19th of January 2017.