Assessing the compact-binary merger candidates reported by the MBTA pipeline in the LIGO-Virgo O3 run: probability of astrophysical origin, classification, and associated uncertainties

We describe the method used by the Multi-Band Template Analysis (MBTA) pipeline to compute the probability of astrophysical origin, $p_{astro}$, of compact binary coalescence candidates in LIGO-Virgo data from the third observing run (O3). The calculation is performed as part of the offline analysis and is used to characterize candidate events, along with their source classification. The technical details and the implementation are described, as well as the results from the first half of the third observing run (O3a) published in GWTC-2.1. The performance of the method is assessed on injections of simulated gravitational-wave signals in O3a data using a parameterization of $p_{astro}$ as a function of the MBTA combined ranking statistic. Possible sources of statistical and systematic uncertainties are discussed, and their effect on $p_{astro}$ quantified.