Fast and Accurate Estimation for Astrophysical Problems in Large Databases

In this proposed thesis, I will develop efficient non-parametric methods for parameter estimation in large databases of high-dimensional, noisy data. Specifically, I plan to continue exploring the efficacy of the diffusion map method of data transformation, used in conjunction with the Nyström extension, in uncovering underlying structure in complicated, high-dimensional data sets. I will explore models that effectively exploit this structure to accurately estimate scientific parameters of interest. Additionally, I will formulate multi-scale methods that generate data-driven bases within local partitions to allow for the modeling of more complicated data. The proposed methods will be tested on three research problems in astrophysics: estimation of star formation history (SFH) in galaxies using spectra from the Sloan Digital Sky Survey (SDSS), photometric redshift estimation using data from the SDSS Photometric Survey and the Canada-France-Hawaii Telescope Legacy Survey, and detection of classes of quasar and outliers using SDSS spectra. Preliminary work has already shown promise in the proposed methods for both SFH estimation (Richards et al. 2009) and photometric redshift estimation (Freeman et al. 2009). 1 Astronomical survey data Technological advancements in observational astronomy have caused a recent flood of astronomical surveys that collect data from billions of objects.1 Modern surveys amass data for different types of astronomical object (e.g. stars, galaxies, quasars) across the entire electromagnetic spectrum, including the radio (FIRST, Becker et al., 1995; NVSS, Condon et al., 1998), microwave (WMAP, Wright et al., 2009), infrared (2MASS, Skrutskie et al., 2006; AKARI, Murakami et al., 2007), optical (SDSS, York et al., 2000; LSST, Becla et al., 2006; Pan-STARRS, Kaiser & Pan-STARRS Team, 2002), ultraviolet (GALEX, Bianchi & The GALEX Team, 1999), X-ray (XMM-Newton, Georgakakis et al., 2003), and gamma-ray (GLAST, Gehrels & Michelson, 1999). Several surveys are dedicated to estimating specific sets of parameters for astronomical objects. For example, the 2dF surveys (Boyle et al., 2001) are dedicated to the accurate estimation of the redshifts of 250,000 galaxies and 25,000 quasars. The DEEP2 survey (Davis et al., 2003) is designed to study the evolution of the properties of galaxies (e.g. mass, metallicity, spatial clustering) as a function of redshift. Larger surveys are often designed to estimate parameters for a broader range of astronomical objects across many astronomical disciplines. For instance, the SDSS survey has see http://www.cv.nrao.edu/fits/www/yp_survey.html for a listing of more than 70 current astronomical surveys with links to information and data products from each.