Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation

2026-10-07

AI Summary

This study addresses the limitations of existing Bayesian inference methods for switching stochastic differential equations (SSDEs), which typically rely on analytical transition densities and are constrained by noise assumptions and dimensionality. To overcome these bottlenecks, this work proposes an approximate Markov chain Monte Carlo (MCMC) sampling framework based on homogenization and factorized neural likelihood estimation (FNLE). By modeling state switching via continuous-time Markov chains and incorporating time-conditioned FNLE, the method achieves general and efficient inference without requiring analytical transition densities, effectively circumventing restrictions to linear drifts and low-dimensional settings. Experiments demonstrate that the proposed approach successfully recovers multi-model parameters on synthetic data and accurately detects state transitions in real-world datasets, thereby validating its broad applicability.

Abstract

Switching stochastic differential equations (SSDEs) describe continuous-time dynamics whose parameters switch according to a latent regime process that follows a continuous-time Markov chain (CTMC). By allowing dynamics to change between regimes, SSDEs represent heterogeneous system behavior and have been applied across diverse fields. However, Bayesian inference for SSDEs remains difficult, and existing SSDE inference methods have limited applicability, with restrictions such as noise-free observations, univariate states, linear drift, or state-independent diffusion. In this study, we propose an approximate Markov chain Monte Carlo sampler for SSDEs using uniformization and factorized neural likelihood estimation (FNLE), a simulation-based inference method. Uniformization provides an exact representation of the CTMC but requires SDE transition densities over arbitrary time intervals. We approximate these densities by training a time-conditioned FNLE model. The resulting sampler is broadly applicable to SSDEs without requiring analytically tractable transition densities. In synthetic-data experiments, our method recovered regime paths and parameters for three SSDE models for which previous methods have limited applicability. We also applied our method to a real dataset and detected a regime transition.

Problem

• Switching Stochastic Differential Equations
• Bayesian Inference
• Markov Chain Monte Carlo
• Simulation-Based Inference

Innovation

• Switching Stochastic Differential Equations
• Approximate MCMC
• Uniformization
• Factorized Neural Likelihood Estimation
• Simulation-Based Inference