# Parameter estimation from an Ornstein-Uhlenbeck process with measurement noise

arXiv: https://arxiv.org/abs/2305.13498 · HTML: https://mlsanity.com/paper/2305.13498/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 3 of 3)

- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Ground-truth resting-state signal provides data-driven estimation and correction for scanner distortion of fMRI time-series dynamics](https://mlsanity.com/paper/2004.06760/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Quantum-Inspired DRL Approach with LSTM and OU Noise for Cut Order Planning Optimization](https://mlsanity.com/paper/2508.16611/) (2025)
- [Robust SDE Parameter Estimation Under Missing Time Information Setting](https://mlsanity.com/paper/2601.20268/) (2026)
- [Bayesian Uncertainty Quantification for fMRI Functional Connectivity via Simulation-Based Inference](https://mlsanity.com/paper/2609.30445/) (2026)

## Abstract (arXiv)

This article aims to investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we propose algorithms and methods that can effectively distinguish between thermal and multiplicative noise and improve the precision of parameter estimation for optimal data analysis. Specifically, we explore the impact of both multiplicative and thermal noise on the obfuscation of the actual signal and propose methods to resolve them. First, we present an algorithm that can effectively separate thermal noise with comparable performance to Hamilton Monte Carlo (HMC) but with significantly improved speed. We then analyze multiplicative noise and demonstrate that HMC is insufficient for isolating thermal and multiplicative noise. However, we show that, with additional knowledge of the ratio between thermal and multiplicative noise, we can accurately distinguish between the two types of noise when provided with a sufficiently large sampling rate or an amplitude of multiplicative noise smaller than thermal noise. Thus, we demonstrate the mechanism underlying an otherwise counterintuitive phenomenon: when multiplicative noise dominates the noise spectrum, one can successfully estimate the parameters for such systems after adding additional white noise to shift the noise balance.