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Relative performance and convergence behavior of FTE vs. FDE estimators under finite data

Determine whether, under finite data sampling, the fixed-time ensemble estimator \(\hat{\Lambda}_1\) and the fixed-divisions ensemble estimator \(\hat{\Lambda}_2\) consistently differ in performance, and characterize how their convergence behaviors depend on the underlying stochastic model for single-cell generation times, including correlations across generations.

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Background

The paper considers two dual approaches to estimate Λ from lineage data: the fixed-time ensemble (FTE) estimator Λ^1\hat{\Lambda}_1, based on division counts NtN_t at fixed time, and the fixed-divisions ensemble (FDE) estimator Λ^2\hat{\Lambda}_2, based on total time TnT_n for a fixed number of divisions.

Both estimators can suffer from systematic errors related to linearization effects and extremal statistics. Prior to the present analysis, it was unclear how their finite-data performance compares across different single-cell models and correlation structures.

References

Although the dual estimator \hat{\Lambda}_2 also appears to have systematic errors from the linearization effect, it is unclear whether one estimator consistently outperforms the other or how their convergence patterns are influenced by specific model details.

— Extremal events dictate population growth rate inference (2501.08404 - GrandPre et al., 14 Jan 2025) in Section 2 (Dual estimators and error decomposition)