Rubin-LSST

Abstract:

We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding the binning of LFs. One challenge in applying KDE to LFs is how to treat the boundary bias problem, as astronomical surveys usually obtain truncated samples predominantly due to the flux-density limits of surveys. We use two solutions, the transformation KDE method ( ) and the transformation–reflection KDE method ( ) to reduce the boundary bias. We develop a new likelihood cross-validation criterion for selecting optimal bandwidths, based on which the posterior probability distribution of the bandwidth and transformation parameters for and are derived within a Markov Chain Monte Carlo sampling procedure. The simulation result shows that and perform better than the traditional binning method, especially in the sparse data regime around the flux limit of a survey or at the bright end of the LF. To further improve the performance of our KDE methods, we develop the transformation–reflection adaptive KDE approach ( ). Monte Carlo simulations suggest that it has good stability and reliability in performance, and is around an order of magnitude more accurate than using the binning method. By applying our adaptive KDE method to a quasar sample, we find that it achieves estimates comparable to the rigorous determination in a previous work, while making far fewer assumptions about the LF. The KDE method we develop has the advantages of both parametric and nonparametric methods.

Abstract:

Evidence for electroweak production of two jets in association with a Zγ pair in s=13 TeV proton–proton collisions at the Large Hadron Collider is presented. The analysis uses data collected by the ATLAS detector in 2015 and 2016 that corresponds to an integrated luminosity of 36.1fb−1. Events that contain a Z boson candidate decaying leptonically into either e+e− or μ+μ−, a photon, and two jets are selected. The electroweak component is measured with observed and expected significances of 4.1 standard deviations. The fiducial cross-section for electroweak production is measured to be σZγjj−EW=7.8±2.0fb, in good agreement with the Standard Model prediction.