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Cross-Modal Multivariate Pattern Analysis
Published on: November 9, 2011
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Fast Bayesian inference of the multivariate Ornstein-Uhlenbeck process.
Rajesh Singh1, Dipanjan Ghosh2, R Adhikari1,3
1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Physical Review. E
|August 17, 2018
Summary
We developed a fast Bayesian method to estimate parameters for the Ornstein-Uhlenbeck process using N observations. This approach accurately analyzes systems like the Brownian harmonic oscillator, aiding colloidal particle research.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- The multivariate Ornstein-Uhlenbeck process models systems returning to a mean state.
- Accurate estimation of its drift and diffusion matrices is crucial for scientific analysis.
Purpose of the Study:
- To present an efficient O(N) Bayesian method for estimating Ornstein-Uhlenbeck process parameters.
- To apply this method to the Brownian harmonic oscillator for parameter estimation and analysis of its dynamics.
Main Methods:
- Utilized exact likelihoods expressed via four sufficient statistic matrices.
- Derived explicit maximum a posteriori (MAP) parameter estimates and standard errors.
- Implemented a Bayesian model comparison for Kramers and Smoluchowski limits.
Main Results:
- Developed an O(N) Bayesian method for drift and diffusion matrix estimation.
- Successfully applied the method to a bivariate Ornstein-Uhlenbeck process (Brownian harmonic oscillator).
- Provided Bayesian estimates for correlation functions and power spectral densities.
Conclusions:
- The novel Bayesian method offers efficient and accurate parameter estimation for Ornstein-Uhlenbeck processes.
- This technique enhances the analysis of inertial motion for systems like colloidal particles in optical traps.
- Bayesian model comparison aids in selecting appropriate physical limits for oscillator models.
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