Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo

Area of Science:

• Statistics
• Computational Neuroscience
• Econometrics

Background:

• Dynamic interactions over time are studied in econometrics, neuroscience, and computational psychology.
• The Wishart process is a Bayesian nonparametric model effective for time-series analysis, but inference is challenging.
• Existing inference methods like MCMC and variational inference have limitations.

Purpose of the Study:

• Introduce a novel Sequential Monte Carlo (SMC) sampler for the Wishart process.
• Compare the performance of the SMC sampler against traditional MCMC and variational inference methods.
• Demonstrate the utility of the proposed method for analyzing dynamic covariance structures.

Main Methods:

• Developed a Sequential Monte Carlo (SMC) sampler tailored for the Wishart process.
• Conducted simulation studies to evaluate estimation and prediction accuracy.
• Applied the SMC sampler to a clinical depression dataset.

Main Results:

• SMC sampling provided the most robust estimates and out-of-sample predictions for dynamic covariance.
• SMC outperformed MCMC and variational inference, particularly with composite covariance functions and correlated parameters.
• The method accurately represented the posterior distribution, enabling effective testing for covariance dynamics.

Conclusions:

• The proposed SMC sampler offers a more robust and accurate inference method for the Wishart process compared to existing approaches.
• This advancement facilitates better modeling of dynamic covariance in various scientific disciplines.
• The approach is practically applicable for analyzing complex time-series data and testing for dynamic changes.