NON-LOCAL PRIORS FOR HIGH-DIMENSIONAL ESTIMATION.

Area of Science:

• Statistics
• High-Dimensional Data Analysis
• Bayesian Inference

Background:

• Achieving both parsimony and predictive power in high-dimensional statistical models is a significant challenge.
• Non-local priors (NLPs) are known for their utility in model selection but their application in parameter estimation requires further investigation.

Purpose of the Study:

• To investigate the estimation properties of Non-local priors (NLPs) in Bayesian model averaging (BMA) for high-dimensional statistical models.
• To develop a constructive representation of NLPs for efficient posterior sampling and extend their applicability.

Main Methods:

• Theoretical analysis of NLP-based BMA for regular and linear models with dimension growing with sample size.
• Constructive representation of NLPs as mixtures of truncated distributions.
• Comparison with benchmark priors (hyper-g) and penalized methods (SCAD, LASSO) via simulations and gene expression data analysis.

Main Results:

• NLP-based BMA demonstrates fast shrinkage rates for spurious parameters and preserves non-spurious ones in high dimensions.
• The proposed NLP representation enables efficient posterior sampling, facilitating high-dimensional linear model estimation (p >> n) with low computational cost.
• NLPs outperformed benchmark methods in reducing estimation error and improving cross-validated R-squared, even without variable pre-screening.

Conclusions:

• Non-local priors are effective for high-dimensional parameter estimation, offering a unified approach for both model selection and estimation.
• The findings challenge the notion that separate priors are necessary for estimation and model selection, suggesting selection priors can be beneficial for estimation.
• NLP-based BMA provides a computationally efficient and accurate method for analyzing complex high-dimensional datasets.