Gaussian Process Modeling of Derivative Curves

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Tracy Holsclaw*+
• Companies: University of California at Irvine
• Keywords: Bayesian statistics ; cosmology ; stochastic process models ; Gaussian process

Abstract

Gaussian process (GP) models provide non-parametric methods to fit continuous curves observed with noise. We develop a GP-based inverse method that allows for the direct estimation of the derivative of a curve. We employ this method to fit the dark energy equation of state, a second derivative process embedded in a non-linear transform when related to the observable data. An inverse method is required to coherently model the dark energy equation of state and relate its fit back to the observed data, which requires two integrations. In general, parametric forms have been used to model the dark energy equation of state because of the complexity of the inverse problem. We show the form of dark energy can be modeled with a non-parametric GP which can be integrated by properties of the stochastic process. This results in a computationally efficient algorithm for the integrations. This inverse statistical method of estimating functions of derivatives with GP is generalizable to many other applications.