Statistics!

At a café not long ago, I overheard some students sitting by me complaining that their error analysis exercise for a physics lab class was  extremely boring (involving e.g. propagation of errors in measurements). Usually, when I hear griping about classes I have to restrain myself from throwing coffee cups, but in this case I wasn’t even tempted. The students were neither whiny nor lazy (and, in fact, were also going on enthusiastically about how interesting and challenging their computer science class was) and, more importantly, I had exactly the same view when I was an undergrad.

Understanding statistics is, of course, important for measurement, which is important for doing physics. It’s also, as at least some of us find out much later, extremely interesting. What are the fundamental limits on how well one can optically determine the position of a molecule, given that it emits some number of photons? How can one determine whether a microscopic particle is moving randomly, or with some directed motion? How can one “read” a graph showing a signal from a new fundamental particle at some level above the background noise, and have a sense of the likelihood of a false detection?

I think what separates the “interesting” questions from the boring way in which statistical methods tend to be introduced in Physics courses is that in the latter, error analysis seems like a way of dotting i’s and crossing t’s — one “knows” the answer from the rest of the experiment, and error propagation, etc., put bounds on it that are important, but not exciting. What would be good to convey to students, though, is that statistical treatments can do much more — they can tell us what the limits are of what can and can’t be measured, and what can and can’t be known!

Statistics is high on the (large) list of topics I wish I had a better understanding of. I’ve been reading Fundamentals of Statistical Signal Processing over the past few weeks to get a more solid grasp of things like Cramer-Rao bounds that I’ve picked up in scattered forms in the past. It’s an excellent book, though it doesn’t have a cover that’s nearly as great as this one: