Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

Area of Science:

• Statistics
• Computational Statistics
• Machine Learning

Background:

• Posterior computation for high-dimensional data presents significant computational challenges.
• Approximating posterior distributions is crucial for statistical inference in complex models.

Purpose of the Study:

• To develop a novel method for approximating posterior distributions of low- to moderate-dimensional parameters.
• To address computational challenges posed by high-dimensional nuisance parameters in regression models.

Main Methods:

• A likelihood decomposition technique using rotation to separate parameters.
• Integration of nuisance parameters via a novel Gaussian approximation.
• Theoretical analysis of approximation accuracy for various priors and nuisance components.

Main Results:

• The proposed method effectively approximates posterior distributions in the presence of challenging nuisance parameters.
• Theoretical guarantees on approximation accuracy are established.
• Empirical validation on simulated and real datasets demonstrates superior performance over state-of-the-art methods.

Conclusions:

• The novel Gaussian approximation offers an efficient and accurate solution for posterior computation in high-dimensional regression.
• This method enhances statistical inference capabilities for complex models.
• The approach shows promise for broader applications in Bayesian statistics and machine learning.