Quantified uncertainty for estimating the bifurcation location u_c in low-data settings

Ascertain procedures by which early warning methods based on statistical model comparison of stochastic dynamical models or machine-learning approaches can estimate the control parameter value u_c at which a bifurcation occurs together with quantified uncertainty (e.g., confidence intervals) when only limited samples per parameter value are available.

Background

Recent EWS methodologies, including statistical model comparison and machine learning, can estimate where a bifurcation occurs. Yet, the paper emphasizes that in realistic low-data regimes—typical in many experiments—it is not clear how such methods can provide estimates accompanied by reliable uncertainty quantification.

This gap affects practical utility because point estimates without confidence intervals or credible intervals hinder risk assessment and decision-making. The authors motivate developing approaches that can work in data-constrained scenarios while delivering rigorous uncertainty measures for u_c.

References

However, in low-data settings typical of many experiments, it remains unclear how these methods can estimate the u value at which the bifurcation occurs with quantified uncertainty (e.g., confidence intervals).

— Detecting and forecasting tipping points from sample variance alone  (2602.10817 - Masuda, 11 Feb 2026) in Introduction (performance of model-based and machine-learning EWSs)

Another important question that should be addressed in the future is the possibility to evaluate these quantities in a real-world context, for instance for the climate system experiencing climate changes.

— Information transfer as a new indicator of approaching local bifurcations: saddle-node, pitchfork and Hopf bifurcations  (2610.17529 - Vannitsem et al., 13 Oct 2026) in Section 6, Conclusions, p. 16