![]() Hennessy, Željko Ivezić, Stephen Kent, Peter Z. Crocker, István Csabai, Mamoru Doi, Douglas Finkbeiner, Scott Friedman, Joshua A. Brinkmann, Robert Brunner, Scott Burles, Larry Carey, Francisco J. ![]() We analyze prediction region coverage properties, large-sample efficiency, and robustness properties of four methods for constructing conformal prediction intervals for GLMs: fully nonparametric kernel-based conformal, residual based conformal, normalized residual based conformal, and parametric conformal which uses the assumed GLM density as a conformity measure.Daniel E. We develop a novel concentration inequality for maximum likelihood estimation in exponential families that induces these convergence rates. In Chapters 4 and 5, we continue our Lyman-$\alpha$ absorption spectroscopy analysis of the intergalactic medium by utilizing the full redshift $z \gtrsim 2.1$ quasar catalog compiled by the Baryon Oscillation Spectroscopic Survey (Dawson et al., 2013) to reconstruct a 47 $h^ rate when d > 2. The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra and (2) constructing observational spectral/light-curve templates. We study the Lyman-$\alpha$ forest in the greatest detail - using trend filtering to map the large-scale structure of the intergalactic medium along one-dimensional quasar-observer sightlines. The astronomical observations we discuss are (1) the Lyman-$\alpha$ forest absorptions in the spectra of high redshift quasars (2) the broader spectroscopic signatures of quasars, galaxies, and stars (3) stellar light curves with planetary transits (4) light curves of eclipsing binary star systems and (5) supernova light curves. Literature and demonstrate its broad utility by discussing how it can contribute to a variety of spectroscopic and time-domain studies. In Chapters 2 and 3, we introduce trend filtering (Tibshirani, 2014) into the astronomical In this dissertation, we study a variety of astrophysical problems of a statistical nature. As the magnitude of these catalogs continues to grow exponentially, the presence of statisticians and computer scientists working at the interface of astronomy and astrophysics becomes increasingly essential to the advancement of the field. quasars and the cosmic microwave background). stars and extrasolar planets) to the extremely remote (e.g. Modern astronomical surveys compile massive catalogs of images, light curves, and spectra that allow us to study the Universe from the relatively local (e.g. Together with bootstrap-based confidence bands for the projection of the meanĬontinuum on a fixed number of principal components, allow us to assess theĭegree of uncertainty in the model predictions. Regression model that have finite sample guarantees. Introduce distribution-free prediction bands for the nonparametric functional Lyman-alpha forest both on simulated spectra and real spectra. Proposed method accurately predicts the unobservable continuum in the Spectrum) are function-valued random variables. The predictor variable (the smooth part of the damping-free portion of the Use a nonparametric functional regression model in which both the response and To predict the continuum in the Lyman-alpha forest, we `continuum' from the noise and the contribution of the damping effect in the To decode the information conveyed by the Lyman-alpha forestĪbout the matter distribution, we must be able to separate the smooth Quasar travels through regions of the Universe with higher matterĬoncentration. Spectrum can be modeled as a noisy realization of a smooth curve that isĪffected by a `damping effect' which occurs whenever the light emitted by the The observed Lyman-alpha forest of a quasar light Galactic nuclei which allows us to probe remote regions of the Universe thatĪre otherwise inaccessible. The Lyman-alpha forest is a portion of the observed light spectrum of distant
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