This week's Statistics Seminar Speaker will be Michelle Carey, who is a postdoctoral researcher in the Department of Biostatistics and Computational Biology at University of Rochester Medical Center.
Talk Title: A generalised smoother for linear ordinary differential equations.
Abstract:
The incorporation of model based penalties in a penalised regression framework (generalised smoothing) has been the subject of many publications, most notably: Cao and Ramsay (2007); Heckman and Ramsay (2000); Ramsay and Silverman (2005); Ramsay et al. (2007). Generalised smoothing facilitates the estimation of the parameters of an ordinary dierential equation (ODE) from noisy data without the specication of an explicit expression of the functional entity described by the ODE. This is a notable consequence of the smoothing procedure however it is not its primary aim. Generalised smoothing aims to obtain an estimated functional entity that adheres to the data and incorporates domain specic information dened by the ODE.
The existing methodology for the estimation of the parameters in generalised smoothing is hindered by the absence of an explicit expression in terms of the parameters of the ODE for the penalty within penalised tting criterion. The aim of this research is to obtain this explicit expression for penalties dened by B{spline basis functions in order to facilitate the development of the estimation procedure.The recursive algorithm developed by de Boor (2001) is the predominant methodology for the evaluation of B-spline basis functions over a given interval. While this algorithm is a fast and numerically stable method for nding a point on a B-spline curve given the domain, it does not explicitly provide knowledge of the internal structure of the B-spline functions. This work introduces an alternative representation of B-spline basis functions in terms of the underlying polynomials that comprise the B-spline. This alterative representaion of B-spline basis functions produces generalised penalties which can be written explicitly in terms of the parameters of the ODE.