The workshop is designed to provide something of value to as wide a range of participants as possible, ranging from those interested in whether FDA might prove useful in their research, to statistical methodologists looking for research problems and interested in new techniques.
The lectures will intersperse case studies with discussions of statistical and mathematical issues.
Each lecture will begin with one or more case studies, and the initial lectures will be almost entirely case studies. These aim to show the range of applications possible, show what insights might be gained from using FDA methods, and illustrate the challenges that are specific or particularly relevant to the analysis functional data. Case studies are not “how to” sessions, but rather address questions like, “Why should I consider this approach?” and “What should I watch out for?”
The first day will also be more oriented to the preliminaries of functional data analysis:
- What are functional data?
- How should they be prepared for analysis?
- How do we convert discrete noisy data to smooth functions?
- What data exploration tools are useful?
- Do the data display both phase and amplitude variation?
- What about principal components analysis and other exploratory methods?
The second day will be primarily given over to linear models for functional data. This is a vast topic, and includes relatively basic topics like functional versions of analysis of variance and regression analysis and as well as issues less familiar to statisticians such as how differential equations can be used to model functional data. All approaches assume that the goal is to explain variation in one or more response variables by variation in one or more input or independent variables where, naturally, at least one of the variables involved is functional.
