Data augmentation-based statistical inference of diffusion processes

Author:

Wang Yasen1ORCID,Cheng Cheng2ORCID,Sun Hongwei2,Jin Junyang3ORCID,Fang Huazhen4ORCID

Affiliation:

1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology 1 , Wuhan, Hubei 430074, China

2. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology 2 , Wuhan, Hubei 430074, China

3. HUST-Wuxi Research Institute 3 , Wuxi, Jiangsu 214174, China

4. Department of Mechanical Engineering, University of Kansas 4 , Lawrence, Kansas 66045, USA

Abstract

The identification of diffusion processes is challenging for many real-world systems with sparsely sampled observation data. In this work, we propose a data augmentation-based sparse Bayesian learning method to identify a class of diffusion processes from sparsely sampled data. We impute latent unsampled diffusion paths between adjacent observations and construct a candidate model for the diffusion processes with the sparsity-inducing prior on model parameters. Given the augmented data and candidate model, we investigate the full joint posterior distribution of all the parameters and latent diffusion paths under a Bayesian learning framework. We then design a Markov chain Monte Carlo sampler with non-degenerate acceptance probability on system dimension to draw samples from the posterior distribution to estimate the parameters and latent diffusion paths. Particularly, the proposed method can handle sparse data that are regularly or irregularly sampled in time. Simulations on the well-known Langevin equation, homogeneous diffusion in a symmetric double-well potential, and stochastic Lotka–Volterra equation demonstrate the effectiveness and considerable accuracy of the proposed method.

Funder

National Key research and Design Program of China

Fundamental Research Funds for the Central Universities

National Natural Science Foundation of China

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Reference45 articles.

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