Large-scale multiple testing under arbitrary covariance dependency and topological data analysis for mass spectrometry imaging applications

This work addresses two highly relevant biomedical questions in the context of Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) data analysis. The first one involves discovering molecular masses that are highly associated with the outcome variable, describing cancer types or subtypes. The second task considered is tumor classification.
The thesis commences with Chapter 1, entitled Synopsis, which provides readers with motivation, presents an overview of the research methods employed, and outlines the remaining content of the thesis. The following two chapters deal with discovering the most associative explanatory variables by means of large-scale multiple testing under arbitrary covariance dependency among test statistics. In a nutshell, these frameworks approximate the false discovery proportion of a thresholding procedure for the marginal p-values. The false discovery proportion represents the proportion of false discoveries among all rejections.
Following this, Chapter 4 addresses the task of tumor classification. Briefly, it introduces a new approach to exploiting peak-related information in the context of MALDI data by employing reduced persistence transformation.
Chapter 5 serves as the concluding discussion of the thesis, drawing conclusions for each of the proposed frameworks, addressing computational challenges in the context of MALDI, outlining contributions, and suggesting future research directions.