Graphical model inference with external network data.

Area of Science:

• Statistics
• Network Science
• Computational Biology

Background:

• Graphical models face challenges with limited sample sizes and interpretability as the number of variables increases.
• External network data can potentially improve inference and model interpretation in graphical models.
• Understanding the interplay between social networks and disease dynamics, such as COVID-19, is crucial.

Purpose of the Study:

• To develop a statistical framework that integrates external network data into graphical models.
• To improve the interpretation, statistical accuracy, and predictive performance of graphical models.
• To investigate the relationship between network structures and graphical model parameters.

Main Methods:

• A spike-and-slab prior framework was developed to model partial correlations based on network structures.
• Regression techniques were used to link edge probabilities, average partial correlations, and their variance to network data.
• Computational schemes and software were developed in R and probabilistic programming languages.

Main Results:

• The proposed framework successfully incorporates network data to enhance graphical models.
• Network data was shown to improve model interpretation, statistical accuracy, and out-of-sample prediction.
• The study demonstrated the utility of the approach in analyzing the co-evolution of COVID-19 across USA counties.

Conclusions:

• Integrating external network data offers a powerful approach to overcome limitations in traditional graphical models.
• The developed framework provides a method to leverage network information for better statistical inference and prediction.
• This approach has significant implications for analyzing complex systems with interconnected variables, including epidemiological studies.