Fast and Robust Likelihood Integration and Sampling of Precessing Compact Binary Coalescence

Our goal is to evaluate and integrate the posterior distribution of compact binary coalescence events, with special interest in precessing signals, at speed and robustness sufficient to make the evidence integral usable as a fully coherent search test statistic, serving as a second-stage search on the many candidates of a traditional match-filtering search pipeline. The method uses a factorization of the likelihood function into components that depend either on intrinsic parameters (masses, spins and inclination) or on extrinsic parameters (sky position, distance, phase, polarization angle and arrival time), but not both. By drawing intrinsic and extrinsic samples, and computing the likelihood components for each, we evaluate the likelihood at all intrinsic-extrinsic pairings through a computationally efficient and trivially parallelizable series of dot products. We reduce the number of likelihood evaluations needed using importance sampling, rejection sampling and quasi Monte Carlo methods, and reduce the number of waveform evaluations needed by pre-computing waveform banks. Beyond efficiency, this method is also less prone to missing modes in the posterior distribution.