Deep follow-up for gravitational-wave inference: a case study with GW151226

New analyses of gravitational wave events raise questions about the nature of some events. For example, LIGO--Virgo--KAGRA initially determined GW151226 to be a merger with a mass-ratio $q\approx0.5$ and effective inspiral spin $\chi_{\text{eff}}\approx 0.2$. However, recent works offer an alternative picture: GW151226 is a lower-mass-ratio event $q \approx 0.3$ with slightly higher spin $\chi_{\text{eff}}\approx 0.3$. This discrepancy has been challenging to resolve as a wide range of differences are employed for each analysis. This work introduces a ``deep follow-up'' framework to efficiently compute the posterior odds between two different peaks in parameter space. In doing so, we aim to help resolve disputes about the true nature of gravitational-wave events associated with conflicting astrophysical interpretations. Our proposal is not a replacement for standard inference techniques; instead, our method provides a diagnostic tool to understand discrepancies between conflicting results. We demonstrate this method by studying three {$q$-$\chi_{\text{eff}}$} peaks proposed for GW151226. We find the $(q\sim0.5, \chi_{\text{eff}}\sim0.2)$ interpretation is only slightly preferred over the $(q\sim0.3, \chi_{\text{eff}}\sim0.3)$ hypothesis with a posterior odds of $\sim1.7\pm0.4$, suggesting that neither of the two peaks can be ruled out. We discuss strategies to produce more reliable parameter estimation studies in gravitational-wave astronomy.