Fridays in MAP 213 from 2:30 PM - 3:30 PM, unless otherwise noted.
Organized by Jason Swanson
| Friday, Feb 12 |
| Paul Jung, Sogang University, Seoul, South Korea |
| Symmetry Breaking in Quasi-1D Coulomb Systems (joint with M. Aizenman) |
We consider systems of negative point charges inside a jellium of uniform positive charge on the tube $[-A,B]\times[-\pi,\pi]$. Let $N(x,\omega)$ denote the signed charge imbalance up to $x$, i.e., on the space $[-A,x]\times[-\pi,\pi]$. We bound the probability of $|N(0)|>\lambda$ uniformly in $A$ and $B$ and show that this probability goes to $0$ as $\lambda\to\infty$. Symmetry breaking follows from a result of Aizenman, Goldstein, Lebowitz (2001).
| Note unusual day/time/location |
| Wednesday, Feb 17 in MAP 318 at 2:30 PM |
| Xiao-Li Meng, Harvard University |
| Self Consistency: A General Recipe for Semi-parametric and Non-parametric Estimation with Incomplete and Irregularly Spaced Data. |
Self-consistency principle, originated by Efron (1967), generalizes MLE for semi/non-parametric estimation with incomplete data and under an arbitrary loss function. It is conceptually appealing, essentially a mathematical formalization of the common-sense “trial-and-error" methods; mathematically elegant, with one fixed-point equation to solve and a general contraction mapping theorem to establish its optimality; and practically straightforward because it directly uses a complete-data method (e.g., LASSO, kernel density estimation) within iterations, much like the EM algorithm. Its major disadvantage is that it can be computationally very intensive. However, increasingly efficient (approximate) implementations are being discovered, such as for wavelet de-noising with hard and soft thresholding. This talk summarizes these findings, based on joint work with Thomas Lee and Zhan Li.
| DEPARTMENTAL COLLOQUIUM |
| Thursday, Feb 18 in MAP 318 at 11:00 AM |
| Xiao-Li Meng, Harvard University |
| Trivial Mathematics but Deep Statistics: Simpson’s Paradox and Its Impact on Your Life |
Few paradoxes have impacted everyday life more than Simpson’s Paradox has. Yet paradoxically, Simpson’s paradox is not even a paradox in the mathematical sense. Simple arithmetic can easily show that it is possible for a surgeon to have the highest overall success rate, and yet have the lowest success rates for each type of surgeries he performed. The fact that you may feel this phenomenon counterintuitive is precisely the reason that the Simpson’s paradox has led to many erroneous conclusions and decisions that affect people’s life, particularly those from social and medical studies, where comparisons using aggregated data are routinely performed. This talk demonstrates the danger of Simpson’s paradox via a number of real-life examples, from the famous Berkeley sex bias case to measuring disparity in mental health service based on the recently released National Latino and Asian American Study (NLAAS), and from batting averages and to the most recent debate on unemployment rates (Wall Street Journal, December 2, 2009). No statistical background is required to understand this talk, but only some common sense and a desire to think deeply beyond formulas.