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.
- 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.
- 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)'.
- 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)'.
- Note the statistics of the distibution in the block at the upper right.
- 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:
- 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).
- 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.
- 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!
- 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.
- 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'.
- For Thursday, April 19: - Prof. Nelson... more on Feldman Cousins.
My notes.
- For Thursday, April 26: - Prof. Nelson... fitting, Chi^2, adding
parameters... part 1 My notes.
- 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.
- For Thursday, May 10: - Prof. Witherell - Discovery & Statistics
- For Thursday, May 17. Maximum likelihood, Cramer Rao. Some useful info, Glen Cowan Lecture 8, Glen Cowan Lecture 9.
- Thursday, May 24 - no meeting
- For Thursday, May 31. Perl Nobel Lecture
- Curt's Resources:Seminar, PRL, Perl Essay
- Perl's earlier articles: Canadian Lecture,
SLAC Summer Institute
- Muon Discovery: Apparatus, Review Paper.
