Author(s): , , , ,
Institution(s): 1. Cornell University, 2. Johns Hopkins University, 3. University of Glasgow
Synoptic time-domain surveys provide astronomers, not simply more data, but a different kind of data: large ensembles of multivariate, irregularly and asynchronously sampled light curves. We describe a statistical framework for light curve demography—optimal accumulation and extraction of information, not only along individual light curves as conventional methods do, but also across large ensembles of related light curves. We build the framework using tools from functional data analysis (FDA), a rapidly growing area of statistics that addresses inference from datasets that sample ensembles of related functions. Our Bayesian FDA framework builds hierarchical models that describe light curve ensembles using multiple levels of randomness: upper levels describe the source population, and lower levels describe the observation process, including measurement errors and selection effects. Schematically, a particular object's light curve is modeled as the sum of a parameterized template component (modeling population-averaged behavior) and a peculiar component (modeling variability across the population), subsequently subjected to an observation model. A functional shrinkage adjustment to individual light curves emerges—an adaptive, functional generalization of the kind of adjustments made for Eddington or Malmquist bias in single-epoch photometric surveys. We are applying the framework to a variety of problems in synoptic time-domain survey astronomy, including optimal detection of weak sources in multi-epoch data, and improved estimation of Cepheid variable star luminosities from detailed demographic modeling of ensembles of Cepheid light curves.