Gaussian process modeling of derivative curves

Gaussian process (GP) models provide nonparametric methods to fit continuous curves observed with noise. In this article, we develop a GP-based inverse method that allows for the direct estimation of the derivative of a one-dimensional curve. In principle, a GP model may be fit to the data directly, with 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 procedure 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 apply it to an important cosmological application. We include a discussion on model comparison techniques for assessing the quality of the fit of this alternative method. Supplementary materials for this article are available online. © 2013 American Statistical Association and the American Society for Quality