**Session title**: **Functional Data Analysis in Action**

**Organizer**: **Kehui Chen (U of Pitt)
Chair:** Kehui Chen (U of Pitt)

**Time:**June 5

^{th}, 1:15pm – 2:45pm

**Location:**VEC 1402

**Speech 1: Brain Functional Connectivity — The FDA Approach**

**Speaker: Jane-Ling Wang (UC Davis)**

**Abstract: **Functional connectivity refers to the connectivity between brain regions that share functional properties. It can be defined through statistical association or dependency among two or more anatomically distinct brain regions. In functional magnetic resonance imaging (fMRI), a standard way to measure brain functional connectivity is to assess the similarity of fMRI time courses for anatomically separated brain regions. Due to the temporal nature of fMRI data, tools of functional data analysis (FDA) are intrinsically applicable to such data. However, standard functional data techniques need to be modified when the goal is to study functional connectivity. We discuss two examples, where a new functional data approach is employed to study brain functional connectivity.

**Speech 2: Functional Data Methods for Replicated Point Processes**

**Speaker: Daniel Gervini (U of Wisconsin at Milwaukee)**

**Abstract: **Functional Data Analysis has traditionally focused on samples of smooth functions. However, many functional data methods can be extended to discrete point processes which are driven by smooth intensity functions. We will review some models that can be used for principal component analysis, joint modelling of discrete and continuous processes, and clustering of spatio-temporal point processes. We will apply these approaches to the analysis of spatio-temporal patterns in the distribution of crime and in the use of the shared-bicycle system in the city of Chicago.

**Speech 3:** **Frechet Regression for Time-Varying Covariance Matrices: Assessing Regional Co-Evolution in the Developing Brain**

**Speaker: Hans Mueller (UC Davis)
Abstract: **Frechet Regression provides an extension of Frechet means to the case of conditional Frechet means and is of interest for samples of random objects in a metric space (Petersen & Müller 2018). A specific application is encountered in cross-sectional studies where one observes $p$-dimensional vectors at one or a few random time points per subject and is interested in the p x p covariance or correlation matrix as a function of time. A challenge is that at each observation time one observes only a $p$-vector of measurements but not a covariance or correlation matrix. For a given metric on the space of covariance matrices, Frechet regression then generates a matrix function where at each fixed time the matrix is a non-negative definite covariance matrix. We demonstrate how this approach can be applied to MRI-extracted measurements of the myelin contents of various brain regions in small infants, aiming to quantify the regional co-evolution of myelination in the developing brain. Based on joint work with Alex Petersen and Sean Deoni.