The course will begin with the problem of estimating a signal in the presence of background when the data consists of counts, a problem of current interest in high energy physics. The problem seems simple, but is surprisingly difficult and raises issues about the foundations of statistics. The remainder of the course will is about estimating an unknown function that is known to obey some shape restrictions, like monotonicity or convexity. Major topics include: convex sets, functions, and optimization; isotonic regression; sampling distributions and tests of hypotheses; some non-parametric problems; and asymptotic distributions. The latter are especially interesting because the limiting distributions are non-normal. The application of shape restricted estimation will be illustrated by considering a problem from astronomy, estimating the distribution of mass in dwarf spheroidal galaxies (How does one weigh a galaxy?). The material on signals and background and the material on convex optimization will function as mini-courses. There will be problem sets, and students will be expected to present a paper. There will be no examinations. The course meets from 11:30 to 1:00 on Tuesdays and Thursdays.
Notes for some selected lectures are available.