# Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems

arXiv: https://arxiv.org/abs/2205.08803 · HTML: https://mlsanity.com/paper/2205.08803/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 60 references that are in the map.
- First posted on arXiv 18 May 2022.

## Builds on (most cited first, 5 of 5)

- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Moment-Based Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/2103.00988/) (2021)
- [Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics](https://mlsanity.com/paper/1402.2584/) (2014)

## Built on by (most cited first, 3 of 3)

- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equations](https://mlsanity.com/paper/2403.04246/) (2024)

## Abstract (arXiv)

Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equation models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.