# Online Bayesian system identification in multivariate autoregressive models via message passing

arXiv: https://arxiv.org/abs/2506.02710 · HTML: https://mlsanity.com/paper/2506.02710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 2 of 2)

- [Reactive Message Passing for Scalable Bayesian Inference](https://mlsanity.com/paper/2112.13251/) (2021)
- [Coupled autoregressive active inference agents for control of multi-joint dynamical systems](https://mlsanity.com/paper/2410.10415/) (2024)

## Built on by (most cited first, 1 of 1)

- [Message passing-based inference in an autoregressive active inference agent](https://mlsanity.com/paper/2509.25482/) (2025)

## Abstract (arXiv)

We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, our method produces full posterior distributions for both the autoregressive coefficients and noise precision. The uncertainties regarding these estimates propagate into the uncertainties on predictions for future system outputs, and support online model evidence calculations. We demonstrate convergence empirically on a synthetic autoregressive system and competitive performance on a double mass-spring-damper system.