Graduate Students Seminar

Speaker 1: Mark Ramos

Title

Power Boosting for Naturally Ordered Multiple Hypotheses

Abstract

A power boosting method is constructed that can be used in combination with existing FDR controlling approaches to provide an extra "boost" of power. It is shown that the power boosting method controls FWER in the weak sense and numerical evidence is provided that under some sparsity assumption, it also controls FDR in the strong sense. Furthermore, numerical evidence shows that the method can be adjusted to be conservative enough so that it can be combined with other FDR controlling approaches at negligible cost to the total nominal level.

Speaker 2: Randy Price

Title

Discrete Data Assimilation for the 2D Navier-Stokes Equations

Abstract

Discrete data assimilation is an area of mathematics with applications in the medical field, weather prediction, prediction of Earth's geomagnetic field, and many more. The Kalman filter, one of the first data assimilation algorithms, was introduced in the 1960's for guidance and navigation systems. Since then more algorithms have come about such as three dimensional variation (3DVar), the ensemble Kalman filter (ENKF), and nudging. In this talk I briefly introduce the mentioned algorithms and discuss numerical results showing how they compare under varying parameters. I will also discuss the various difficulties in implementing the algorithms for the 2D Navier-Stokes equations.