Develop a residual-weighted mass summary statistic

Develop and evaluate a residual-weighted summary statistic for the per-posterior-draw fuzzy-dark-matter masses that down-weights poorly fitted, high-residual realizations rather than discarding them.

Background

The force-balance regression produces an implied boson mass for every converged pyGravSphere posterior draw, together with a reduced force-balance residual. The paper finds that high-mass tails are preferentially associated with large residuals, indicating poor agreement with the assumed static equilibrium condition.

The reported per-galaxy summaries currently treat the converged draws without residual-based weighting. The authors therefore leave open the construction of a statistic that incorporates fit quality, suggesting exponential or inverse-residual weights as examples.

References

A natural refinement, which we identify here but leave for future work (Sec.~\ref{sec:discussion}), is a residual-weighted summary statistic -- for example a weighted median of ${m_{21}{(j)}}$ with weights $w_j \propto \exp(-S_j/n_{\rm used},j})$ or $w_j \propto (S_j/n_{\rm used},j}){-1}$ -- which would down-weight, rather than discard, the poorly-fit high-residual draws responsible for the high-$m_{21}$ tail identified above.

— Hydrostatic Equilibrium Constraints on the Fuzzy Dark Matter Mass from Dwarf Spheroidals: Method, Systematics, and Robustness  (2610.21722 - Mitra et al., 15 Oct 2026) in Section 6.1, subsection “Force-balance residual”