Incorporating spatial structure into inclusion probabilities for Bayesian variable selection in generalized linear...

Area of Science:

• Statistics
• Computational Biology
• Neuroimaging

Background:

• Spike-and-slab priors are used for variable selection in statistical modeling.
• Existing methods like spike-and-slab lasso (SSL) for Generalized Linear Models (GLM) do not fully leverage spatial correlations in data.
• Incorporating spatial structure can enhance model performance, especially with imaging or spatial data.

Purpose of the Study:

• To develop a novel spatial spike-and-slab method for variable selection.
• To integrate spatial information into the prior probabilities of parameter inclusion.
• To improve model fitness and accuracy by accounting for spatial dependencies.

Main Methods:

• Proposed a spatial spike-and-slab approach using intrinsic autoregressive priors on logit prior probabilities of inclusion.
• Adapted a computationally efficient coordinate-descent-based EM algorithm for model fitting, avoiding computationally intensive MCMC.
• Validated the method through a simulation study and an application to Alzheimer's Disease imaging data.

Main Results:

• The proposed spatial method demonstrated improved model fitness compared to non-spatial approaches.
• Incorporating spatial information led to more effective variable selection by considering parameter clustering.
• The adapted EM algorithm provided an efficient way to fit the complex Bayesian models.

Conclusions:

• Integrating spatial information into spike-and-slab priors is beneficial for variable selection in models with spatial data.
• The developed method offers improved accuracy and efficiency for analyzing complex datasets, particularly in neuroimaging and genomics.
• This approach enhances the utility of spike-and-slab methods for spatially correlated data.