Colloquium
The Department of Statistics

presents

Stephanie Land
Assistant Professor
Department of Statistics
Carnegie Mellon University

Regression methodology to relate hormone curves to age

Abstract

The focus of this talk is the analysis of data from a study of aging and circadian rhythms. Hormone measurements taken nearly continuously over a period of two days are related to subjects' ages. I will discuss methods for signal regression, that is, regression in which the predictive information is in the form of signals or curves, as is the hormone data. In our example, the repeated hormone measurements are treated as a large set of predictor variables. The regression problem is therefore ill-posed and requires regularization. Most of the work in signal regression employs regularization designed for smooth relationships between predictors and response. I will discuss the most popular of these methods, cubic spline regression. I will propose new methodology that targets the problems in which the relationship between predictors and response is not globally smooth. The method I propose, variable fusion, produces models of a simple parsimonious form, more readily explained to the non-statistician than other high-dimensional multivariate methods. Variable fusion regularizes by exploiting the spatial nature of the predictor variable index through variable bandwidth nonlinear smoothing analogs based on adaptive splines.