Physics 509C --- Theory of Measurement

(Also known as: how to get the most from your data without making a fool of yourself.)

Term: September 2011
Lecturer: Scott Oser
Class coordinates: Tuesdays/Thursdays, 9:30-11:00 in Hennings 302
Office Hours: Tuesdays 12-1pm, or by appointment
TA: Shimpei Tobayama

Topics covered: Interpretation of probability; basic descriptive statistics; common probability distributions; Monte Carlo methods; Bayesian analysis; methods of error propagation; systematic uncertainties; parameter estimation; hypothesis testing and statistical significance; confidence intervals; blind analyses; methods of multivariate analysis; non-parametric tests; periodicity searches; "robust" statistics; deconvolution and unfolding

Prerequisites: Officially, none. However, you will be expected to have some facility with computational techniques and programming in a high-level language, or at least a willingness to learn very quickly. Quite simply, it's not possible to do much data analysis or statistics without being able to program. Almost all homework assignments will have a large computational component, although this class will not teach programming per se. If you don't already know basic computational physics, your time might be better spent taking Physics 210 or Physics 410 instead.

Textbooks: There are two textbooks for this course:

1. Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, by Roger Barlow

2. Bayesian Logical Data Analysis for the Physical Sciences, by P.C. Gregory

Each has a different focus with different strengths and weaknesses, and I'll draw on material from both.

Supplemental material: You may also find these books enlightening:

• Numerical Recipes, by William H. Press (available online here)

• Statistical Data Analysis, by Glen Cowan

• Practical Statistics for Astronomers, by J.V. Wall and C.R. Jenkins

• Probability and Statistics, by Morris H. DeGroot

Your grade will be determined by:

Homework	60%
Midterm	20%
Final Exam	20%

Homework: There will be approximately five lengthy homework assignments. They will generally include analytic calculations, essay-type questions, and computational problems that will require you to analyze data sets and most usually to write some computer code to do so. You are welcome to discuss problems informally with your classmates. However, you must complete the assignment yourself, and if you hand in obviously copied homework, you should expect a mark of zero on that assignment, or worse. Assignments are due by the end of class on the day they are due. I will give more guidelines in class for how to submit completed assignments.

Useful software: This course will require some computational facility on your part. The entire course can be done using free software, and you're not required to buy anything. The most important things you'll need are access to a good plotting package and a library of scientific routines (capable of random number generation, non-linear fitting, and matrix operations at a minimum). I encourage you to use whatever tools your field uses or that you already know, but if you want some recommendations, you may find the following useful:

1. ROOT: a combined plotting/analysis package developed by the high energy physics community (but of general utility), based on a C++ interpreter. Extremely powerful, with decent tutorials available. Free. Includes most numerical routines you might want, and since it's based on C++ it can work with other libraries or code as well.

2. gnuplot: a free plotting package with some basic fitting capability (although not enough to do every HW problem). This might be a good option if you're writing standalone code in C/C++/FORTRAN and just need a way of plotting the output.

3. Mathematica: an integrated plotting and mathematical analysis package. Quite expensive (prohibitively so if you're not a student). A single user license for an old, slow version of Mathematica 4 is available on the main physics server.

4. GNU Scientific Library: a free library of computational routines. To some extent it is a freeware equivalent of the routines in Numerical Recipes. Available in C and C++.

5. Numerical Recipes: Very commonly used. Although the text of the book is available online for free, the routines are proprietary, and you're supposed to buy the book if you use any of the routines. Available in C, C++, and FORTRAN.

Programming languages: It's up to you to choose what programming language you feel most comfortable with. These days I'd generally recommend C++, as it is quickly coming to dominate many areas of the physical sciences, and most libraries of scientific routines are available in that language. But I will confess that I am personally still much more fluent in FORTRAN and C. If you want to use something besides C++, C, or FORTRAN, please be my guest, but I won't be able to offer you much specific advice on coding issues. Not that I will anyway.

Missed exams: There will be one in-class midterm exam. If you miss the exam with a legitimate excuse (proof of illness, family emergency, etc), see me to discuss make-up options.

Religious holidays: Students are entitled to request an alternate test date if a scheduled test date falls on one of their holy days. If you think this may apply to you, please contact me as soon as possible to make an alternate arrangement. Please don't put this off until the last minute---you must give at least two week's notice.

FINAL EXAM: The final exam is not yet scheduled. A take-home exam is a likely possibility.

Syllabus: A tentative lecture schedule follows. It will almost certainly be adjusted as the course proceeds.

Scott Oser (email me) June 22, 2011