Chaotic Bayesian Inference: Strange Attractors as Risk Models for Black Swan Events
The paper presents a dual-model framework for chaotic inference and rare-event detection. Model A, using Poincaré–Mahalanobis, focuses on geometric structure for stable inference. Model B, employing Correlation–Integral with Fibonacci diagnostics, emphasizes recurrence statistics and volatility clustering. The Lorenz–Lorenz experiments show that diagnostic weighting shifts inference from stability to rare-event focus. The Lorenz–Rössler experiments demonstrate Model B’s generalization across attractors, maintaining sensitivity to volatility. The framework combines stable geometric anchoring with robust rare-event detection, advancing systemic risk analysis. Future work aims to extend the models to higher-dimensional systems, optimize computational efficiency, and apply them to finance, climate, and infrastructure.