Introduction to Functional Data Analysis

Module code: MA4202

This module introduces methods for Functional Data Analysis (FDA) with an emphasis on practical issues and applications. It introduces to students the concept of functional data and the methodologies for analysing such data. The preferred software for this course will be R programming. And this course will explore and demonstrate the FDA techniques based on the R packages.

Classical statistics deal with observations that consist of a single characteristic or attribute, or multiple measurements for each subject. Functional data analysis deals with data in the form of curves or surfaces that can be conceptualised as samples of an underlying continuous stochastic process, such as temperature over time, growth curves, stock prices over time, etc. The object of the FDA is usually considered to be infinite-dimensional, often (but not always) with some inherent smoothness characteristics. FDA has been applied to a wide range of areas such as chemistry, business, astronomy, medicine, meteorology, social science, etc. In this module we will study both the theory behind functional data analysis and the methodologies developed to analyse such data in the myriad of different fields where this type of data arises. The primary objective of this module will be the applications of FDA techniques to real-world problems, and thus, the students are required to understand both the established methods and the newly adopted techniques. Beginning with the basics for the analysis of data that may be considered to be ‘functions’, this module will discuss various visualisation, data exploration, and statistical inference techniques. Specifically, the module will introduce the concepts of functional data, representation of functional data, spline smoothing techniques, functional principal components analysis, and functional linear models. Students will be required to work on an applied project based on real functional data sets.