In recent decades, functional data analysis has emerged as a significant field for examining data that vary continuously, such as curves and images. Features in functional data often exhibit variations in both shape (amplitude) and timing (phase), which are typically intertwined and difficult to separate. In a forthcoming publication in the Journal of the Royal Statistical Society Series B: Statistical Methodology, Professor Jimin Ding and her former doctoral student, Tian Wang, introduced a new concept of separability and proposed a novel model to address this long-standing challenge.
The proposed method allows users to flexibly adjust the focus of modeling between vertical features (e.g., peaks and valleys in a curve) and horizontal features (e.g., timing shifts). This approach offers a fresh perspective on the issue of identifiability and effectively resolves common sources of ambiguity. The model decomposes complex functional features into four components: amplitude shape, phase change, scale, and shift. By applying this powerful tool to real-world COVID-19 infection data, the authors were able to uncover hidden functional patterns in the infection rates and provide insights into clustering states into different subgroups.
Tian Wang completed her PhD at WashU in 2018 and is currently a research staff member at the Department of Biostatistics, Mailman School of Public Health, Columbia University. Please visit the journal website for the original article.
