Validate the Bayesian asymmetry posterior for Poisson noise

Validate whether the correlated-noise Bayesian asymmetry posterior remains unbiased for Poisson noise by constructing a representative synthetic data set that simultaneously samples the flat asymmetry prior and repeating the coverage test.

Background

The Bayesian asymmetry posterior is derived and validated for uniform Gaussian noise, including an approximate treatment of spatially correlated noise caused by beam convolution. Poisson noise is not directly treated because its noise geometry depends on the underlying signal, so the simple synthetic flux model used for the Gaussian coverage test would not provide a convincing validation.

The authors identify a concrete unresolved task: construct a representative synthetic sample whose asymmetries follow the adopted flat prior while also reproducing the signal-dependent structure of Poisson noise, and then use that sample to test the posterior’s coverage. They state that completing this construction would require extensive work and defer it to a future study.

References

It would be possible to verify how well Equation \ref{eq:bayes_asym_full} applies to Poisson noise by repeating the coverage test for Poisson noise. However, since the geometry of the noise would then depend on the underlying signal, simply using the Equation~\ref{eq:synthetic_flux} would be unconvincing; the synthetic images used would need to be representative of the actual data. The construction of such a sample which would simultaneously sample the prior $p(a)=\chi_{[0,1]}(a)$ would require extensive work that we leave for a future study.

— Bayesian Galaxy Asymmetry  (2609.26472 - Perron-Cormier et al., 22 Sep 2026) in Section 2.4, “Extension to Correlated Bins” (Section \ref{sec:reduced_magnitude})