Tracy Holsclaw DISSERTATION DEFENSE: Statistical Modeling for Dark Energy And Associated Cosmological Constants

Friday, May 27, 2011
10:00 am, E2-506 (LANL T226, 11:00 am)

DISSERTATION DEFENSE: Statistical Modeling for Dark Energy and Associated Cosmological Constants

Tracy Holsclaw
Friday, May 27, 2011,

Hosted by Herbie Lee
Applied Mathematics & Statistics

10:00 am, Engineering 2, Room 506 (UCSC)

Video-conference locations

  • Los Alamos National Lab: Room T-226, 11:00 am
  • Argonne National Lab: Room F-240, 12 noon

Abstract

Our endeavor has been to answer one of science's important questions, mainly about the nature of dark energy. We have worked along side cosmologists to better understand our Universe and in due course have developed some useful statistical methods for undertaking analysis of derivative processes, model selection, and experimental design. There are no direct measures available for the posited dark energy; its form must be inferred from other data sources like supernova, cosmic microwave background radiation, or baryon acoustic oscillation. The dark energy equation of state is 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 Gaussian process 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 Gaussian processes is generalizable to many other applications. Additionally, we show the benefits of this modeling for the dark energy equation of state through model comparison methods that can handle both parametric and non-parametric models. Finally, we compare future data collection missions using the Gaussian process model in an experimental design setting.

Faculty Advisors: Bruno Sanso, Herbie Lee

LANL Mentors: Katrine Heitman, David Higdon