Statistical inference for persistent homology applied to simulated fMRI time series data

Time-series data are amongst the most widely-used in biomedical sciences, including domains such as functional Magnetic Resonance Imaging (fMRI). Structure within time series can be captured by tools of topological analysis (TDA). Persistent homology is mostly commonly used data-analytic tool TDA, and effectively summarize complex high-dimensional into an interpretable 2-dimensional representation called a persistence diagram. Existing methods for statistical inference persistent depend on independence assumption being satisfied. While computed each index time-series, time-series often fail to satisfy assumption. This paper develops test that obviates implementing multi-level block sampled Monte Carlo with sets diagrams. Its efficacy detecting task-dependent organization then demonstrated simulated fMRI data. new therefore suitable analyzing data, non-independent general.