Chaotic Bayesian Inference: Strange Attractors as Risk Models for Black Swan Events

ArXiv ID: 2509.08183 “View on arXiv”

Authors: Crystal Rust

Abstract

We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches: Model A, which emphasizes geometric stability, and Model B, which highlights rare bursts using Fibonacci diagnostics. Together, they provide a dual perspective for systemic risk analysis, linking Black Swan theory to practical tools for stress testing and volatility monitoring.

Keywords: Bayesian Inference, Chaos Theory, Volatility Clustering, Heavy-Tailed Distributions, Stress Testing

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced mathematics, including chaotic dynamics, Bayesian inference, and complex geometric diagnostics, while the empirical evidence is limited to simulated data without real-world backtests or implementation details.

  flowchart TD
    A["Research Goal: Model Black Swan Events"] --> B{"Data: Historical Volatility &<br>Extreme Event Distributions"}
    B --> C["Methodology: Chaotic Bayesian Inference"]
    C --> D["Model A: Lorenz Dynamics<br>Geometric Stability"]
    C --> E["Model B: Rossler Dynamics<br>Fibonacci Rare Bursts"]
    D --> F["Computational Process:<br>MCMC Sampling<br>Strange Attractors"]
    E --> F
    F --> G["Outcomes: Volatility Clustering<br>Heavy Tails & Stress Testing"]