Discussion of paper by K. Garside et al.

We discuss the paper Garside et al. (2020). Although topological data analysis (TDA) has been around for many decades with well grounded theoretical development, it still suffers from numerous statistical and computational issues. For these reasons, it has not yet become a standard tool for data scientists. The authors point out the difficulty of directly applying existing statistical models to persistent homology due to the heterogeneous nature of topological features. The statistical development in TDA in the last decade has been focused on making heterogeneous features into homogenous structured data by transformations or smoothing. The main achievement is that stability results on such transformed topological features have been established. Thus, the idea of applying survival analysis techniques to the birth and death process of topological feature is very intriguing. The authors succeed in elucidating the connection between the event history methods and the life time of topological features. However, the paper has stimulated new interesting questions.