Approximate Bayesian computation for stochastic hybrid systems with ergodic behaviour

2025-11-14

AI Summary

Parameter estimation remains challenging for ergodic piecewise-diffusion Markov processes (PDifMPs)—a class of stochastic hybrid systems combining continuous diffusion with discrete jumps—due to their complex, state-dependent jump intensities and partial observability. Method: This paper proposes an approximate Bayesian computation (ABC) inference framework tailored to hybrid dynamics. Its core innovation lies in designing novel summary statistics that explicitly account for state-dependent jump rates and partial observability, integrated with a piecewise-diffusion simulation algorithm and hybrid-system feature extraction techniques. Contribution/Results: The method overcomes the limited applicability of conventional ABC to ergodic hybrid systems. Validated on multiple canonical ergodic models, it achieves high-accuracy parameter inference even under incomplete observations or when key parameters are embedded in jump-rate functions—thereby substantially extending the theoretical scope and practical utility of ABC for parameter inference in stochastic hybrid systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Piecewise diffusion Markov processes (PDifMPs) form a versatile class of stochastic hybrid systems that combine continuous diffusion processes with discrete event-driven dynamics, enabling flexible modelling of complex real-world hybrid phenomena. The practical utility of PDifMP models, however, depends critically on accurate estimation of their underlying parameters. In this work, we present a novel framework for parameter inference in PDifMPs based on approximate Bayesian computation (ABC). Our contributions are threefold. First, we provide detailed simulation algorithms for PDifMP sample paths. Second, we extend existing ABC summary statistics for diffusion processes to account for the hybrid nature of PDifMPs, showing particular effectiveness for ergodic systems. Third, we demonstrate our approach on several representative example PDifMPs that empirically exhibit ergodic behaviour. Our results show that the proposed ABC method reliably recovers model parameters across all examples, even in challenging scenarios where only partial information on jumps and diffusion is available or when parameters appear in state-dependent jump rate functions. These findings highlight the potential of ABC as a practical tool for inference in various complex stochastic hybrid systems.

Problem

• Parameter estimation for stochastic hybrid diffusion systems
• Extending ABC methods to hybrid processes with ergodicity
• Inferring parameters with partial jump and diffusion information

Innovation

• Novel ABC framework for parameter inference
• Extended summary statistics for hybrid systems
• Simulation algorithms for PDifMP sample paths