# Online Probabilistic Model Identification using Adaptive Recursive MCMC

arXiv: https://arxiv.org/abs/2210.12595 · HTML: https://mlsanity.com/paper/2210.12595/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Variational Bayesian Decision-making for Continuous Utilities](https://mlsanity.com/paper/1902.00792/) (2019)
- [Bayesian Nonparametric Spectral Estimation](https://mlsanity.com/paper/1809.02196/) (2018)
- [A Fast and Scalable Joint Estimator for Integrating Additional Knowledge in Learning Multiple Related Sparse Gaussian Graphical Models](https://mlsanity.com/paper/1806.00548/) (2018)

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

- [Fuel Consumption Prediction for a Passenger Ferry using Machine Learning and In-service Data: A Comparative Study](https://mlsanity.com/paper/2310.13123/) (2023)
- [Deep Reinforcement Learning-based Intelligent Traffic Signal Controls with Optimized CO2 emissions](https://mlsanity.com/paper/2310.13129/) (2023)
- [LeTFuser: Light-weight End-to-end Transformer-Based Sensor Fusion for Autonomous Driving with Multi-Task Learning](https://mlsanity.com/paper/2310.13135/) (2023)

## Abstract (arXiv)

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which eliminates the shortcomings of conventional online techniques while computing the entire probability density function of model parameters. The limitations to Gaussian noise, the application to only linear in the parameters (LIP) systems, and the persistent excitation (PE) needs are some of these drawbacks. In ARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution is proposed. The forgetting factor can be presented adaptively using the TFF in many dynamical systems as an alternative to a constant hyperparameter. By offering a trade-off between exploitation and exploration, the specific jump distribution has been optimised towards hybrid/multi-modal systems that permit inferences among modes. These trade-off are adjusted based on parameter evolution rate. We demonstrate that ARMCMC requires fewer samples than conventional MCMC methods to achieve the same precision and reliability. We demonstrate our approach using parameter estimation in a soft bending actuator and the Hunt-Crossley dynamic model, two challenging hybrid/multi-modal benchmarks. Additionally, we compare our method with recursive least squares and the particle filter, and show that our technique has significantly more accurate point estimates as well as a decrease in tracking error of the value of interest.