Stein's Paradox, Lemma, and Method
Consider the estimation of three unrelated quantities, such as the speed of light, your daily coffee consumption, and
Kingston's COVID activity level. The James–Stein estimator proposes to estimate them simultaneously and borrow
information across them. For normally distributed data, it beats, in terms of the sum of quadratic losses, the most
natural approach, which estimates each quantity individually. We prove this counter-intuitive result using Stein's
lemma.
The reverse direction of Stein's lemma characterizes the standard normal distribution, It motivates a family of powerful techniques now called Stein's method for bounding distances between probability distributions. We discuss the basic idea behind the method.
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Welcome to the Math Club home page!
The math club meets once a week in the Winter term, on Thursday evenings for about an hour. It is intended for anyone interested in mathematics, whether they are a math major or not.
At each meeting a speaker will discuss an interesting idea in mathematics. We try to pick topics that can be understood without much background. An ideal topic is one which starts with something simple, and by exploring its twists and turns, leads to something unexpectedly deeper.
The goal is to show mathematics the way that mathematicians see it: a living subject full of deep and intertwining ideas, growing naturally out of our desire to understand the fundamental concepts of space and number.
Date | Topic | Speaker | |||
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Jan. | 25 | The century of elliptic curves | M. Ram Murty | ||
Feb. | 1 | Pascal's Hexagrammum Mysticum | David Wehlau | ||
8 | Bifoliations of the plane from bifoliations of the circle | Thomas Barthelmé | |||
15 | What is the average area of the shadow of a cube? | Mike Roth | |||
29 | Proof of the sensitivity conjecture | Ivan Dimitrov | |||
Mar. | 7 | Stein's Paradox, Lemma, and Method | Yanglei Song | ||
14 | TBA | Jamie Mingo | |||
21 | CANSSI Distinguished Lecture | Xiao-Li Meng (Harvard) | |||
28 | TBA | Francesco Cellarosi | |||
Apr. | 4 | From the Angels and Devils game to the control of wildfires | Teresa Chiri |
The meetings are Thursdays in Jeff 118 from 17:30–18:30.
To suggest a topic for the Math Club, or to find out further information, please email Ivan Dimitrov, Mike Roth, or Greg Smith .
Web Site of the Week |
Check out Quanta Magazine; an online science magazine specializing in Mathematics, Physics, and the Life Sciences. |
Winter 2024 |
Queen's University |
Kingston, Ontario |