Functional Data Analysis (FDA) is a class of statistical methods that apply to repeated, complex processes. Classical examples include motion capture data in which subjects repeat the same action several times. These actions are recorded with very high frequency and accuracy, but will differ from repeat to repeat and from subject to subject. Because the process are complicated, they are modeled as non-parametric functions of time; methods in FDA are used to describe variation between curves and relationships between these curves and other quantities. While motion capture data serves as a useful motivation, FDA can be applied in a wide variety of applications and does not require precise or high-frequency measurements of every curve.
This course will introduce participants to the statistical methods of Functional Data Analysis modeling, and to computational tools to carry them out. We will briefly review techniques for nonparametric smoothing to represent individual functions before developing methods to describe distributions of functions and variation between them. The course will examine extensions of linear regression, generalized linear models and generalized additive models to the cases where functional data serve either as covariates or as a response. We will also describe methods in two areas unique to FDA: curve alignment, in which we try to match the timing of features between different curves, and dynamics in which a derivative of the function, or relationships between derivatives, serve as the relevant question of interest.
The course will provide example code that makes heavy use of the fda package in R; further software resources that replicate or extend this functionality will be cited.