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  • Open Access

Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable

Javier Aguilar*

Miguel A. Muñoz†

Sandro Azaele†

  • Dipartimento di Fisica e Astronomia Galileo Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy, and Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain

  • Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain

  • *Contact author: javiersanguilar@gmail.com
  • †Leadership of the research was shared among the senior authors.
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Phys. Rev. X 16, 031015 – Published 23 July, 2026

DOI: https://doi.org/10.1103/tmkr-9kl2

Abstract

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes to deliver reliable parameter estimation and model selection from coarsely sampled time series, without requiring analytical solutions. Crucially, we couple mechanistic stochastic models with their inference procedures to quantify how experimental design—specifically, sampling frequency and dataset size—governs estimator precision and model distinguishability. This analysis reveals optimal sampling regimes and sharp, resolution-dependent limits beyond which competing models become empirically indistinguishable. We validate the approach across four disparate systems—trajectories of optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population time series—recovering parameters and identifying when inference is fundamentally constrained by measurement resolution, thereby clarifying ongoing debates about dominant noise sources in these systems. Together, these results establish path-based Monte Carlo as a practical, general tool for inference and model discrimination in complex systems and provide principled guidelines for designing measurements that maximize information under real-world constraints.

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Popular Summary

From the diffusion of particles to the growth of forests, capturing the randomness of complex systems often relies on simple, interpretable mathematical models. We introduce a path-inference framework combining Monte Carlo sampling with information-theoretic tools to establish how data collection protocols govern parameter precision and model discrimination. Our approach reveals sharp, resolution-dependent limits beyond which mathematically distinct models become empirically indistinguishable. Testing this framework across data from optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population datasets allows us to identify optimal sampling regimes and clarify ongoing debates regarding dominant noise sources. Ultimately, these results establish principled limits of inference in complex systems and provide guidelines for experimental design to maximize the information retrieved from real-world data.

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Phys. Rev. X 16, 031015– Published 23 July, 2026
  • Received 3 October 2025
  • Accepted 21 May 2026
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