Statistical Engineering Division Seminar

Dr. Katharine M. Mullen
Department of Physics and Astronomy
Vrije Universiteit Amsterdam
Teusday, May 20, 2008, 10:45-11:45 AM
Building 222, Room A330

Abstract

Models consisting of a linear superposition of non-linear functions with a Gaussian distributed noise term are used to describe data arising in a wide variety of applications. The inverse problem associated with estimating the most likely values for the linear and nonlinear parameters of such a model is an instance of separable nonlinear least squares, which is possible to address with the variable projection algorithm due to Golub and Pereyra and variants thereof. The rapid and accurate solution of separable nonlinear least squares problems has become increasingly important in the physical sciences, as improvements in instrumentation have made data resolved with respect to many experimental variables more common. Multi-way data is often possible to describe in selected experimental variables in terms of a nonlinear parametric model, while in other experimental variables a parametric description may be not feasible or desirable. In such situations a separable nonlinear model may be used to describe the data in all experimental variables simultaneously. In this talk I will discuss applications of separable nonlinear models in time-resolved fluorescence microscopy of cells in vivo, as well as in ultra-fast time-resolved spectroscopy and mass spectrometry. I will also discuss the implementation of a framework for the specification and optimization of separable nonlinear models in the R package TIMP for the R language and environment for statistical computing.