Seminar Supervisor

Prof. Dr. Evgeny Spodarev

Seminar Advisor

Duc Nguyen, M. Sc.

Date and Place

Depending on the number and preferences of the participants we will meet weekly or in blocks.  
Place: TBA.

Prerequisites

The level of difficulty in this seminar is varying between the different topics. The audience is at least supposed to be familiar with basic probability, statistics, basic analysis and measure theory. We ensure the participants that most of the 'beyond' knowledge will be learned during the seminar.

Intended Audience

Bachelor and Master students in any mathematical programme of studies. 

Content

 

In this seminar, we will uncover the essence of empirical Bayes reasoning—a powerful combination of statistical approaches that holds promise for tackling modern research and real-world challenges. With practical applications in economy, biostatistics, and data science, we will witness its impact on making data-driven decisions. Discover the fundamental concepts of false discovery rates, relevance assessment, and handling the correct null hypothesis. This seminar seeks to provide a comprehensive understanding of empirical Bayes methods and their potential significance in shaping the future of large-scale statistical analyses. 

The first three talks will be about the Bayesian approach for large-scale hypothesis testing, which provides a coherent and probabilistic framework to analyze and draw inferences from multiple hypotheses simultaneously. Therefore, these talks aim to provide students an overview pictures about fundamental concepts in multiple comparison procedures (MCP) context such as p-values, z-values, family-wise error (FWER), false discovery rate (FDR) and so on. 

• Talk 1:  James-Stein Estimator.
• Talk 2: Large-scale Hypothesis Testing.
• Talk 3: Significance Testing Algorithm.

In the next three talks, we'll discuss about controlling FDR, which is more flexible and useful in different fields. We'll also discuss the importance of Local False Discovery Rate (lfdr) control, a major focus nowadays. However, due to the fact that a test is nothing without a deep understanding about the null distribution of test statistic, therefore, one of the talk will be focus on this aspect.

• Talk 4: False Discovery Rate Control.
• Talk 5: Local False Discovery Rate.
• Talk 6: Theoretical, Permutation and Empirical Null Distribution.

In practice, the assumptions of our input data following specific distributions or being independent are often not met. Hence, estimation and correlation become crucial when implementing the Multiple Comparisons Procedure (MCP). The next three talks aim to explore how we can use information about the data to improve the efficiency of our tests. We'll focus on understanding the null distribution of the test statistic and the dependency structure to achieve this goal.

• Talk 7: Estimation Accuracy.
• Talk 8: Correlation Questions.
• Talk 9: Combination, Relevance, and Comparability.

The seminar will consist of 9 talks, but we are open to adding more topics if there is sufficient interest from students. It is essential to highlight that these 9 talks will focus on multiple comparison procedures. Additionally, we encourage students or groups to consider providing one or two talks based on the course "MIT 18.650 Statistics for Applications, Fall 2016" by Rigollet. This course provides a solid foundation in single hypothesis testing, making it easier to approach multiple comparison procedures.

• Talk 0: Parametric Hypothesis Testing.

Registration

To register for the seminar, please write an E-Mail to Duc Nguyen until October , 13. In the e-mail please give your name, matriculation number, your programme of studies and subjects you have taken in the area of Probability or Statistics. Furthermore, after we have the final list of participants, we will arrange a meeting to discuss what topic that you are interested in.

Criteria to pass the seminar

Each student or group is supposed to give a talk. Those who give a (good) talk together with written summary will pass the seminar. Talks will be held in English. A preliminary version of the Slides need to be submitted two weeks before each talk.

Literature

[1] Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction (2010) by Efron.

[2] Computer Age Statistical Inference, Algorithms, Evidence, and Data Science (2021) by Efron and Hastie.

[3] Controlling the False Discovery Rate - A Practical and Powerful Approach to Multiple Testing (1995) by Benjamini and Hochberg.

[4] Multiple Testing Procedures with Applications to Genomics (2009) by Dudoit, J. van der Laan.

[5] The course "MIT 18.650 Statistics for Applications, Fall 2016" by Rigollet.

[6] The edge of discovery: Controlling the local false discovery rate at the margin (2022) by Soloff, Xiang and Fithian.