UCSC-SOE-11-02: Gaussian Process Modeling of Derivative Curves

Tracy Holsclaw, Bruno Sanso, Herbert Lee, David Higdon, Katrin Heitmann, Ujjaini Alam and Salman Habib
01/12/2011 09:00 AM
Applied Mathematics & Statistics
Gaussian process (GP) models provide non-parametric methods to fit continuous curves observed with noise. In this paper, we develop a GP based inverse method that allows for the estimation of the derivative of a curve, avoiding direct estimation from the data. A GP model can be fit to the data directly, then the derivatives obtained by means of differentiation of the correlation function. However, it is known that this approach can be inadequate due to loss of information when differentiating. We present a new method of obtaining the derivative process by viewing this as an inverse problem. We use the properties of a GP to obtain a computationally efficient fit. We illustrate our method with simulated data as well as with an important cosmological application. We include a discussion on model comparison techniques for assessing the fit of this alternative method.