  Over the last two decades, topological data analysis (TDA) has emerged as a
very powerful data analytic approach which can deal with various data
modalities of varying complexities. One of the most commonly used tools in TDA
is persistent homology (PH) which can extract topological properties from data
at various scales. Our aim in this article is to introduce TDA concepts to a
statistical audience and provide an approach to analyze multivariate time
series data. The application focus will be on multivariate brain signals and
brain connectivity networks. Finally, the paper concludes with an overview of
some open problems and potential application of TDA to modeling directionality
in a brain network as well as the casting of TDA in the context of mixed
effects models to capture variations in the topological properties of data
collected from multiple subjects
