Model cross-shell stochastic covariance

Extend the BOLTS model for tomographic analyses by replacing independent per-shell stochastic draws with a cross-shell stochastic covariance that accounts for correlations between adjacent redshift shells caused by line-of-sight structure and projection.

Background

The present BOLTS implementation treats every redshift shell independently and imposes uncorrelated stochastic draws between distinct shells. However, adjacent thin shells are physically correlated because projected structures extend along the line of sight.

Tomographic applications, including 3×2-point analyses, require a joint treatment of these shell-to-shell correlations. The paper identifies promotion of the per-shell stochastic variance to a cross-shell covariance as the proposed unresolved extension.

References

For tomographic analyses such as $3{\times}2\mathrm{pt}$, the framework can be extended by promoting the per-shell stochastic variance to a cross-shell covariance. We defer this to future work.

— An analytical model for non-local stochastic field-level galaxy bias on the sphere  (2610.12259 - Wietersheim-Kramsta et al., 8 Oct 2026) in Section 6, Conclusions