Jordan Schupbach Ph.D. Proposal in Statistics (Dept. of Mathematical Sciences, MSU)

06/13/2022

Abstract: 

Topological data analysis (TDA) is an interdisciplinary field that seeks to represent the shape of data using tools from algebraic topology. However, methods for analyzing these representations under non-trivial sampling designs are few to non-existent. As a result, statistical inference is rarely employed in practice and estimates of uncertainty typically assume independence
when conducting predictive inference. In this talk, methods for conducting statistical and predictive inference in TDA for hierarchical sampling designs are proposed. In particular, collections of persistence diagrams (a common topological descriptor) given by a hierarchical sampling design are proposed to be modeled as a replicated mixed-effect inhomogeneous point process.  With this model, we propose how predictive and statistical inference can be conducted in TDA and we propose some solutions to computational issues that arise in this context.