Oct 9

3:30 pm

## Sharpening Buffon\'s Needle

### Michael Perlman

Seminar

University of Washington - Department of Statistics

In 1733, Buffon posed and solved perhaps the first problem in geometric probability: what is the probability p that a needle of length l, when dropped at random on a grid of parallel lines separated by distance d, crosses a line (l< d) ? Buffon's solution, using the new integral calculus, was a landmark not only in continuous probability theory but also in statistical estimation theory: because p = 2l/(\pi)d, this experiment could be performed to yield empirical estimates of \pi. This experiment and many variants performed by Buffon's successors provide an amusing glimpse into the early days of statistics.

We shall examine two particular variants, performed with two or three sets of parallel lines, in which modern statistical theory can be used to "sharpen" Buffon's needle by yielding estimates of \pi with dramatically increased efficiency. We discuss both the design of the experiments and the determination of "sufficient statistics," which utilize the available statistical information as fully as possible.

Refreshments to follow in the Statistics lounge, 3rd floor, Padelford.