Jim Ramsay is a Professor Emeritus of Psychology and an Associate Member in the Department of Mathematics and Statistics at McGill University. He received a Ph.D. from Princeton University in 1966 in quantitative psychology. He served as Chair of the Department from 1986-1989.
Jim has contributed research on various topics in psychometrics, including multidimensional scaling and test theory. His current research focus is on functional data analysis, and involves developing methods for analyzing samples of curves and images. The identification of systems of differential equations from noisy data plays an important role in this work.
He has been President of the Psychometric Society and the Statistical Society of Canada. He received the Gold Medal of the Statistical Society of Canada in 1998 and the Award for Technical or Scientific Contributions to the Field of Educational Measurement of the U. S. National Council on Measurement in Education in 2003.
The workshop is aimed at those who might want a sense of what the field of functional data analysis is all about, but have no need to understand its mathematical aspects. The concepts and challenges in the field will be illustrated by a variety of data analysis problems. The lectures will draw on a recent book aimed at applications: Ramsay, J. O., Hooker, G. and Graves, S. Functional Data Analysis with R and Matlab, that was published by Springer in 2009.
We will do a grand tour of the most important issues in the analysis of functional data, illustrating along the way what we mean by “functional” in referring to data. A variety of types of data will be displayed along with some results, without much attempt to explain how these results were obtained. The idea of the derivative of a function will be introduced and illustrated briefly for those with either nonexistent or badly rusted calculus backgrounds, and the pivotal roles that derivatives play in functional data analysis will be illustrated.
Lecture 2: Data smoothing
The data that we work with to explore functional structure are seldom actually functional themselves. Instead, they come to us as discrete and usually noisy measurements, of the variety that we have traditionally called “repeated measures” in the social sciences. The challenge is to use these data to estimate a set of smooth functions, often with derivatives that we can use in various ways. We show how to estimate functions by explicitly controlling the smoothness of the function that we estimate.
Hands-on Workshop (limited seats available)
In the afternoon we’ll work together on some live data sets such as growth data, and investigate the properties of various ways of smoothing the data to obtain a function that fits the data to an appropriate level. Problems that we will explore will include how to choose the basis function system, how many basis functions to use, how to choose knots for spline basis functions, and how to choose a value of the smoothing parameter. We will also generate some simulated data so that we can see how well our smoothing strategies work when we know the right answer.
Further information can be found at www.psych.mcgill.ca/misc/fda.