Misspecification in amortized X-ray spectral inference: a detection benchmark, a gain shift three schemes cannot see, and marginalizing it out
Abstract
Amortized neural posterior estimation fits X-ray spectra in milliseconds, and pipeline use will lean on post-hoc checks to catch detector systematics the simulator misses. We measure what those checks see, on simulated spectra from real XMM-Newton EPIC-pn and NICER responses. Of four misspecification families, an unmodelled 6.4 keV line and partial covering are catchable per spectrum (AUC 0.97 and 0.84). A wrong continuum family reaches 0.66. One flow passed every recovery check yet under-covered (coverage deviation 0.114), and a converged NICER flow (0.011) fails simulation-based calibration on all five parameters. Recovery metrics do not certify calibration. Three schemes catch the line: the posterior-predictive check, importance sampling against the exact Poisson likelihood (effective sample size, 0.68-0.82), and the nested-sampling evidence (count-controlled, −67 to −892 nats). None catches the 3 per cent gain shift, 2.4 to 14.4 times the EPIC-pn energy-scale accuracy (AUC 0.44-0.54; 36-cell means 0.50 and 0.49 on both responses; paired evidence +0.33 ± 1.37 nats). The effective sample size stays null-consistent from 0.1 to 10 per cent, realistic amplitudes included. The shift still biases the photon index by +0.02 (0.03 to 0.11σ) at both count levels. Retraining with a per-simulation nuisance gain adds no inference-time cost, and the gain posterior returns the prior. The bias survives, and exact gain-marginalized nested sampling shows the flow capturing at most 0.163 of its gain constraint (continuous-prior convention) at high counts. Marginalization over posited calibration nuisances is the working defence for X-ray SBI at catalog scale; no check we ran supplies a warning.
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BibTeX
@misc{akbari2026misspecification,
title = {{Misspecification in amortized X-ray spectral inference: a detection benchmark, a gain shift three schemes cannot see, and marginalizing it out}},
author = {Karan Akbari},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.17098},
eprint = {2606.17098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17098},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Misspecification in amortized X-ray spectral inference: a detection benchmark, a gain shift three schemes cannot see, and marginalizing it out
AU - Karan Akbari
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2606.17098
UR - https://arxiv.org/abs/2606.17098
AB - Amortized neural posterior estimation fits X-ray spectra in milliseconds, and pipeline use will lean on post-hoc checks to catch detector systematics the simulator misses. We measure what those checks see, on simulated spectra from real XMM-Newton EPIC-pn and NICER responses. Of four misspecification families, an unmodelled 6.4 keV line and partial covering are catchable per spectrum (AUC 0.97 and 0.84). A wrong continuum family reaches 0.66. One flow passed every recovery check yet under-covered (coverage deviation 0.114), and a converged NICER flow (0.011) fails simulation-based calibration on all five parameters. Recovery metrics do not certify calibration. Three schemes catch the line: the posterior-predictive check, importance sampling against the exact Poisson likelihood (effective sample size, 0.68-0.82), and the nested-sampling evidence (count-controlled, −67 to −892 nats). None catches the 3 per cent gain shift, 2.4 to 14.4 times the EPIC-pn energy-scale accuracy (AUC 0.44-0.54; 36-cell means 0.50 and 0.49 on both responses; paired evidence +0.33 ± 1.37 nats). The effective sample size stays null-consistent from 0.1 to 10 per cent, realistic amplitudes included. The shift still biases the photon index by +0.02 (0.03 to 0.11σ) at both count levels. Retraining with a per-simulation nuisance gain adds no inference-time cost, and the gain posterior returns the prior. The bias survives, and exact gain-marginalized nested sampling shows the flow capturing at most 0.163 of its gain constraint (continuous-prior convention) at high counts. Marginalization over posited calibration nuisances is the working defence for X-ray SBI at catalog scale; no check we ran supplies a warning.
ER -