Stabilizing simulation-based cosmological Fisher forecasts: a case study using the Voronoi volume function

TL;DR

This paper presents a framework to stabilize and optimize cosmological Fisher forecasts using summary statistics like the Voronoi volume function, improving constraint accuracy and stability in limited simulation scenarios.

Contribution

The authors introduce a systematic method to stabilize derivative estimates and select optimal summary statistics, enhancing the reliability of cosmological forecasts from limited simulations.

Findings

Improved constraining power by up to a factor of 4

Enhanced stability of forecasts across realizations

Effective use of the Voronoi volume function as a summary statistic

Abstract

Forecasting cosmological constraints from halo-based statistics often suffers from instability in derivative estimates, especially when the number of simulations is limited. This instability reduces the reliability of Fisher forecasts and machine learning based approaches that use derivatives. We introduce a general framework that addresses this challenge by stabilizing the input statistic and then systematically identifying the optimal subset of summary statistics that maximizes cosmological information while simultaneously minimizing the instability of predicted constraints. We demonstrate this framework using the halo mass function as well as the Voronoi volume function (VVF), a summary statistic that captures beyond two-point clustering information. Applying our two-step procedure -- random sub-sampling followed by optimization -- improves the constraining power by up to a factor of 4, while also enhancing the stability of the forecasts across realizations. As surveys like Euclid, DESI, and LSST push toward tighter constraints, the ability to produce stable and accurate theoretical predictions is essential. Our results suggest that new summary statistics such as the VVF, combined with careful data curation and stabilization strategies, can play a key role in next-generation precision cosmology.