@article{abdallah_statistical_2023, abstract = {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 data can be captured by the tools of topological data analysis ({TDA}). Persistent homology is the mostly commonly used data-analytic tool in {TDA}, and can effectively summarize complex high-dimensional data into an interpretable 2-dimensional representation called a persistence diagram. Existing methods for statistical inference for persistent homology of data depend on an independence assumption being satisfied. While persistent homology can be computed for each time index in a time-series, time-series data often fail to satisfy the independence assumption. This paper develops a statistical test that obviates the independence assumption by implementing a multi-level block sampled Monte Carlo test with sets of persistence diagrams. Its efficacy for detecting task-dependent topological organization is then demonstrated on simulated {fMRI} data. This new statistical test is therefore suitable for analyzing persistent homology of {fMRI} data, and of non-independent data in general.}, author = {Abdallah, Hassan and Regalski, Adam and Kang, Mohammad Behzad and Berishaj, Maria and Nnadi, Nkechi and Chowdury, Asadur and Diwadkar, Vaibhav A. and Salch, Andrew}, date = {2023-03-01}, doi = {10.3934/fods.2022014}, journaltitle = {Foundations of Data Science}, keywords = {1 - medicine:{fMRI}, 2 - Hypothesis testing, 2 - Persistent homology, 2 - Statistical inference, 3 - Time series:{fMRI}, 3 - {fMRI}, Innovate}, langid = {english}, note = {Publisher: Foundations of Data Science}, number = {1}, pages = {1--25}, rights = {http://creativecommons.org/licenses/by/3.0/}, shortjournal = {{FoDS}}, title = {Statistical inference for persistent homology applied to simulated {fMRI} time series data}, url = {https://www.aimsciences.org/en/article/doi/10.3934/fods.2022014}, urldate = {2024-01-12}, volume = {5} }