Implement Probability Estimator of Astronomical Events in G-wave Search

Laser Interferometer Gravitational-Wave Observatory (LIGO) is one of the leading experiments in detecting cosmic gravitational wave. Using the wave templates of binary systems from numerical relativity, LIGO have found 90 gravitational wave events whose signals are generated by binary black hole coalescence (BBH), binary neutron star coalescence (BNS), and neutron star – black hole coalescence (NSBH). GstLAL is one of the searching programs developed for identifying G-wave events in the noise data. As the number of gravitational wave sources are increasing with more observation, how to accurately estimate the probability of the astronomical source of a detected event becomes a necessary question. Although there has been theoretical work on how to calculate this probability, the GstLAL team at Penn State carries out a data-based approach to this estimation and implements a software tool to complete the computation. The software infrastructure is necessary in order to handle the large dataflow from LIGO O4 observation which is expected to find over hundreds of gravitational wave events. The statistic principle behind this method is the Bayes Theorem: P(A|B) = P(B|A)P(A)/P(B) where A serves as some detected data of gravitational wave, and B is one of the categories in BBH, BNS, and NSBH. Probability of data given category P(B|A) and probability of data P(A) are postulated from our G-wave database, while probability of category P(B) is treated as a marginalized term. The estimated probability of category given data P(A|B) is used to determine the candidacy of our observed events, along with the comparison from theoretical calculation. This probability estimator is currently implemented to the offline search of LIGO O4 run.