Rapid Hubble constant inference from GW170817 using GPU-accelerated nested sampling: prior sensitivity and the limits of post-hoc reweighting

The bright-siren measurement of the Hubble constant from GW170817 (Abbott et al. 2017) assumes that switching from a volumetric to a uniform-in- d L luminosity-distance prior can be implemented by post-hoc reweighting of the baseline samples, rather than by re-running the inference under the target prior. Using a GPU-native heterodyned nested sampling pipeline that completes the full n live=5000 analysis in about 13 min on a single A100, we recompute the GW170817 H 0 posterior under four prior variants for the modern aligned-spin tidal waveform IMRPhenomXAS NRTidalv3. Switching from the volumetric to a uniform-in- d L distance prior raises the high-tail probability P(H 0>120, km/s/Mpc) from 0.017 to 0.159 when imposed during sampling and shifts the weighted-median H 0 from 77.6 to 87.6 km/s/Mpc, while the binned MAP stays at 70.5 km/s/Mpc: both the tail and the bulk move under a change of prior that leaves the mode in place. Post-hoc reweighting of the baseline samples to the same target prior recovers only P=0.041 in the tail, approximately 17% of the directly sampled shift. The three prior variants that carry an independent nested sampling evidence agree to Z 1.8, so the data show at most a weak preference among the distance priors; the tail and bulk shifts are therefore properties of the prior, not a data update. Targeted mode-isolated runs reveal a (d L, iota) bimodality whose high- H 0, low- d L branch (Mode B; B B/A<1) the volumetric prior assigns negligible mass: this is the mechanism behind the reweighting deficit. The reweighted posterior has a lower effective sample size than the baseline, independently flagging the coverage failure. The runtime budget makes full-sample prior-sensitivity reruns the default robustness tool for bright-siren cosmology, replacing post-hoc reweighting.