Physics 594, Spring 2012 - Profs. Nelson, Witherell

Meeting time finalized to... Thursdays 11am-1pm in 5233 Broida.

This is an 2-unit informal seminar on probability and statistics for high energy physics. We will use various Web resources and notes... our goal is to transmit an intuitive understanding of this topic, and provide references to more formal presentations.

We will endeavor to understand pertinent topics including statistical errors and probability, limits, parameter estimation, goodness of fit, discovery, and maybe case studies in successful and unsuccessful discovery.

Ideally we'll get an introduction to Root, Roofit, and RooStats. We will discuss this more at the first course meeting. However, Prof. Nelson has downloaded, built, and installed these tools on his Mac, and those in this class should do so on their laptops too!

Plan is to meet Tuesdays at 1:30-3:30pm in 5233 Broida.

  1. For Tuesday, April 3... meet and get organized.
    The Poisson distribution. A very intuitive derivation (probably due to Enrico Fermi) is in this excerpt from Segre. The context of that era (1950's, 1960's) is embedded in the derivation: measuring lifetimes of radioactive nuclei. However, the discussion of how long to measure signal, and how long to measure background leads into the contemporary topic of how to quantify possible signals in the presence of background, when the number of signal events is small. Problems 5-8, 5-9, and 5-10 would be good to try.

    We've put together two Root macros to enable one to play with the Poisson distribution.

    1. poissoninit.C to set up and make a fill of a histogram with a Poisson distribution. It takes three arguments... first is the mean of the Poisson (real), the second is the number of experiments (integer), and the third is the histogram maximum (integer). So to call this from Root, you enter something like `.x poissoninit.C(5.,1000,20)'.
    2. poissonup.C to update the histogram started with the previous command. It takes two arguments... first is the mean of the Poisson (real), and the second is the number of experiments (integer). So to call this from Root, you enter something like `.x poissonup.C(4.,1000)'.
    3. Note the statistics of the distibution in the block at the upper right.
    4. To delete the histogram, in Root, enter `h1->Delete();'. To make the y axis logarithmic, `gPad->SetLogy(1)', and to go back to linear `gPad->SetLogy(0)'.

    Another thread that emanates from the Poisson distribution is: it eventually becomes Gaussian for large values of the mean (see discussion starting on page 183 of Segre). This is the first example of the `Central Limit Theorem' we'll encounter. The Gaussian distribution is a sort of universal limiting probability distribution, and underpins most of the basic thinking about statistics and thinking in experimental physics. You can study the transition with Root and the macros above.

    There are many more formal starting points for a discussion of probability:

    1. A favorite, very compact and to the point, but by physicists not mathematicians: graduate lecture notes from Steve Ahlen and Greg Tarle. There is a heuristic proof of the Central Limit Theorem on page 15 (the sixth page in order... 9 are missing from the beginning).
    2. The bible for particle physicists is the Review of Particle Physics (RPP). In the 2011 edition, Glen Cowan contributed this review, as well as this one on statistics, both of which are extremely useful. The style is more formal and mathematical now than in Segre's era. The 1982 RPP review on probability and statistics, as well as the 1992 RPP review show a bit of the evolution of the thinking. One famous quote that pertains, attributed to the founding director of Fermilab Robert Wilson, is, ``The experiment didn't go too well, so, we had to use statistics.'' When experiments see clear signals, the qualitative conclusion is easy. Statistics becomes important when the signals aren't so clear, or when you are trying to precisely nail down a parameter; this has been the situation in particle physics for the last 20 or 30 years.
    3. Glen Cowan teaches many courses on probability and statistics in particle physics. This is the home page of his current course. We will shamelessly borrow and build upon his sterling work!
    4. Here are two more useful references: a very early set of notes (dating from 1958, revised in 1982) by by Jay Orear, and quite contemporary and fun by Art Snyder.

  2. For Thursday, April 12 - Prof. Nelson EVOing (or backup, Skyping) in from South Dakota. Feldman and Cousins... get right to estimating confidence intervals in Bayesian and Frequentist philosophies. My notes. The EVO Conference is `Physics 594 UCSB'.
  3. For Thursday, April 19: - Prof. Nelson... more on Feldman Cousins. My notes.
  4. For Thursday, April 26: - Prof. Nelson... fitting, Chi^2, adding parameters... part 1 My notes.
  5. For Thursday, May 3. Fitting part 2... Billoir/Kalman, updating on the fly...My notes., RPP on passage of particles through matter, Classic from 1964.
  6. For Thursday, May 10: - Prof. Witherell - Discovery & Statistics
  7. For Thursday, May 17. Maximum likelihood, Cramer Rao. Some useful info, Glen Cowan Lecture 8, Glen Cowan Lecture 9.
  8. Thursday, May 24 - no meeting
  9. For Thursday, May 31. Perl Nobel Lecture
    1. Curt's Resources:Seminar, PRL, Perl Essay
    2. Perl's earlier articles: Canadian Lecture, SLAC Summer Institute
    3. Muon Discovery: Apparatus, Review Paper.