Data augmentation-based statistical inference of diffusion processes.

Area of Science:

• * Computational Physics
• * Statistical Modeling
• * Data Science

Background:

• * Identifying diffusion processes is difficult with limited, sparsely sampled data.
• * Real-world systems often present challenges due to incomplete observation datasets.
• * Existing methods struggle with the inherent sparsity in observational data.

Purpose of the Study:

• * To develop a robust method for identifying diffusion processes from sparse data.
• * To address the challenge of imputing unobserved diffusion paths.
• * To enhance the accuracy of diffusion model parameter estimation.

Main Methods:

• * A data augmentation-based sparse Bayesian learning framework is proposed.
• * Latent diffusion paths are imputed between observed data points.
• * A sparsity-inducing prior is utilized for model parameter estimation.
• * A Markov chain Monte Carlo (MCMC) sampler is designed for posterior distribution sampling.

Main Results:

• * The method accurately estimates parameters and reconstructs latent diffusion paths.
• * It effectively handles both regularly and irregularly sampled sparse data.
• * Simulations demonstrate high accuracy on benchmark diffusion models.

Conclusions:

• * The proposed Bayesian learning method offers a powerful solution for diffusion process identification with sparse data.
• * The technique is versatile and applicable to various time-series analyses.
• * This work advances the capability to model complex systems with limited observations.