Exclusive Content & Downloads from ASQ

Gaussian Process Modeling of Derivative Curves

Summary: 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.

Anyone with a subscription, including Site and Enterprise members, can access this article.

Other Ways to Access content:

Join ASQ

Join ASQ as a Full member. Enjoy all the ASQ member benefits including access to many online articles.

  • Topics: Engineering
  • Keywords: Nonparametric methods, Noise, Gaussian curve, Curve fitting, Inverse regression, State space models, Computation, Comparison
  • Author: Holsclaw, Tracy; Sansó, Bruno; Lee, Herbert K. H.; Heitmann, Katrin; Habib, Salman; Higdon, David; Alam, Ujjaini
  • Journal: Technometrics