An exact analytic expression is derived for the joint distribution of effective spins χeff and χp under isotropic uniform spin priors, and a GWTC-3 reanalysis shows the previous KDE approximation can shift log-likelihoods by order one.
Akutsu et al., Progress of Theoreti- cal and Experimental Physics 2021, 05A101 (2020), https://academic.oup.com/ptep/article- pdf/2021/5/05A101/37974994/ptaa125.pdf
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An analytical joint prior for effective spins for inference on the spin distribution of binary black holes
An exact analytic expression is derived for the joint distribution of effective spins χeff and χp under isotropic uniform spin priors, and a GWTC-3 reanalysis shows the previous KDE approximation can shift log-likelihoods by order one.