Graduate Student Seminar

Speaker 1: Jing Wang

Title

The analysis of analyses: An introduction of Meta-analysis

Abstract

TA meta-analysis is a statistical analysis that combines the results of multiple scientific studies. The basic idea of this technique is to produce a weighted average of the included study results, which is considered as a pooled estimate closest to the unknown common truth. In addition, meta-analysis also has the capacity to contrast results from different studies and identify patterns among study results, sources of disagreement among those results, or other interesting relationships that may come to light in the context of multiple studies. A key benefit of this approach is the aggregation of information leading to a higher statistical power https://en.wikipedia.org/wiki/Statistical_power and more robust point estimate than is possible from the measure derived from any individual study. However, in performing a meta-analysis, an investigator must be very careful with deciding how to search for studies, selecting studies, dealing with incomplete data, analyzing data and accounting for publication bias.

Speaker 2: Abhishek Balakrishna

Title

The Hille-Yosida Theorem

Abstract

In this seminar we will talk about the Hille-Yosida Theorem.  We will discuss the proof of the theorem that can be used to approach differential equations involving unbounded linear operators. In the process we will also discuss the definition and properties of semigroups and how they play a key role in the proof.