Graduate Students Seminar

Speaker 1: Abhishek Balakrishna

Title

Data assimilation for the 3–D Boussinesq equation

Abstract

Data assimilation is a method to combine observational data with a model in order to improve the model. In the talk, I will introduce a particular data assimilation technique (AOT algorithm) and provide some intuition for the mathematical framework. The algorithm will then be used to assimilate data (type 1 interpolation) into the 3-D Boussinesq equation, after which the well-posedness and other properties of the solution will be investigated. Lastly, the exponential convergence of the data assimilated solution to the actual solution will be established.

Speaker 2: Yewon Kim

Title

Simultaneous testing of grouped hypotheses

Abstract

Modern statistical inference processes commonly involve testing hundreds of or thousands of hypotheses simultaneously. When testing many hypotheses at the same time, it is mainly aimed at controlling the false discovery rate (FDR) introduced by Benjamini & Hochberg (1995) or local FDR defined by Efron et al. (2001). In most cases, these processes take into account the joint distribution of the test statistics or p-values, as well as additional information such as the grouped structure of hypotheses that can increase the power of the test. In particular, Liu et al. (2016) provides a two-stage multiple testing process called Two fold Loop Testing Algorithm (TLTA) using grouped hypotheses. In this presentation, we will mainly review TLTA with medium-scale data and check the limitations of applying TLTA to large-scale data.