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. Um and and obviously uh I don't think you can use this um tennis court to to observe different stuff that has zero relationships, right? Because the overlap between these two references to two liter, there's almost no overlap.The Lyman-alpha forest is a portion of the observed light spectrum of distant So you would arrange of course observations to detect uh stands in this range, right? In this uh in this spectrum around this spectrum. So still this last in the visible spectrum. Right? And you know, this is um really something you can still observe, right? Because we can see something like 400-760 nm. Right? And that is About if you plug your your body is around 120 nm roughly.
![quasar spectra quasar spectra](http://vertassets.blob.core.windows.net/image/85efb127/85efb127-65e0-4da3-ae81-5844b5cc98b0/pr___quasar_15_color.jpg)
Where um according to this question, if you subtract lambda by lambda north and develop a lambda north, you should get 4.21 right? And from this, you see that the real shifted lambda should be 5.1 and lambda node.
![quasar spectra quasar spectra](https://2.bp.blogspot.com/-b_LxTmojEc8/WyFTlfu2SaI/AAAAAAAAEKc/eQigiakq44ggcuLHzk7NbvVynrK60-TwQCLcBGAs/s1600/quasar%2Bdyes.png)
That means if the rest of reverence Of the emission of the radiation of the study is 121 according to the question Nanometer. And this question you look at a lot shifts of right now, imagine you have a which is a star, right? It has rather shifted Z equals delta lambda over lambda is 4.1.