401 – Astrostatistics Interest Group: Student Paper Award
Trend Filtering: A Modern Statistical Tool for Time-Domain Astronomy and Astronomical Spectroscopy
Collin Politsch
Carnegie Mellon University
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly varying intensity that is occasionally interrupted by abrupt dips or spikes. Likewise, in the spectroscopic setting, a noiseless spectrum typically contains intervals of relative smoothness mixed with localized higher frequency components such as emission peaks and absorption lines. In this work, we present trend filtering, a modern nonparametric statistical tool that yields significant improvements in this broad problem space of denoising spatially heterogeneous signals. When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data—including kernels, LOESS, smoothing splines, Gaussian process regression, and many other popular methods. In the spirit of illustrating the broad utility of trend filtering, we discuss its relevance to a diverse set of spectroscopic and time-domain studies. The observations we discuss are (1) the Lyman- forest of quasar spectra; (2) more general spectroscopy of quasars, galaxies, and stars; (3) stellar light curves with transiting exoplanet(s); (4) eclipsing binary light curves; and (5) supernova light curves. We study the Lyman- forest in the greatest detail—using trend filtering to map the large-scale structure of the intergalactic medium along quasar-observer sightlines. The remaining studies broadly center around the themes of using trend filtering to estimate observable parameters and generate spectral/light-curve templates.