Flexible Bayesian Product Mixture Models for Vector Autoregressions.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Bayesian non-parametric methods, such as Dirichlet process mixtures, excel at information sharing via sample clustering.
• Existing methods struggle with heterogeneous data where clustering occurs along subsets of features or parameters.

Purpose of the Study:

• To develop a novel class of product of Dirichlet process location-scale mixtures.
• To enable independent clustering at multiple scales for flexible information sharing.
• To extend these methods for multivariate time-series data within multi-subject Vector Autoregressive (VAR) models.

Main Methods:

• Developed product of Dirichlet process location-scale mixtures for multivariate data.
• Generalized the approach to multi-subject Vector Autoregressive (VAR) models for time-series data.
• Established posterior consistency and developed efficient posterior computation algorithms.

Main Results:

• Demonstrated superior performance over competing methods in estimation, clustering, and feature selection accuracy via extensive numerical studies.
• Identified biologically interpretable connectivity differences in resting-state fMRI data from the Human Connectome Project between intelligence groups.
• Showcased superior forecasting accuracy in an air pollution application compared to alternative methods.

Conclusions:

• The proposed product of Dirichlet process location-scale mixtures effectively addresses limitations of existing Bayesian non-parametric models in heterogeneous settings.
• The generalized VAR framework offers significant advantages for multivariate time-series analysis.
• The methods provide robust and interpretable insights across diverse scientific domains.