Parameter estimation from an Ornstein-Uhlenbeck process with measurement noise
This work addresses noise separation in parameter estimation for stochastic processes, which is incremental as it builds on existing methods like HMC with specific enhancements for noise types.
The paper tackles the problem of parameter estimation in an Ornstein-Uhlenbeck process affected by measurement noise, specifically multiplicative and thermal noise, and proposes algorithms to separate these noise types and improve estimation accuracy, demonstrating that adding white noise can enable successful parameter estimation when multiplicative noise dominates.
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.