Research

My research is focused on variable selection methods in functional regression models.

“What is functional data?”

A bunch of curves.

“Huh?”

The major difference is that your usual flavor of statistics is about dealing with data points; with functional data, you now have data curves instead.

You’ve seen a scatter plot before, yes? In a scatter plot, each dot is basically an instantaneous snapshot of each individual data point. Let’s say you’re looking weight vs. age. In this instance, every subject only has one data point for those things; e.g., at this very moment, I only have one weight and one age, and at this very moment, you only have one weight and one age.

Still with me? Good.

Imagine tracking something that continuously changes with time, space, frequency, or some other continuum. Each dot is still an instantaneous snapshot, but each subject has their own bunch of dots instead of just one. In our example above, we could look at weight vs. age over time—rather than just our weight and age right now. Now, since we’re tracking things over time, the individual points on their own aren’t necessarily interesting, but they can ideally be considered as having arisen from an underlying smooth curve or function of time, and that is what we are interested in. That’s functional data.

As an simple example, the equivalent iris or mtcars data set for illustrating functional data is the average daily temperature at 35 weather stations across Canada,¹ shown in the plot below (keep me far away from any place named “Uranium City”):