Scalable Bayesian Regression with Massive and High-dimensional Data

1395 

Contributed Abstract 

Poster 

Gyeongmin Park (1), Gyuhyeong Goh (2), Dipak Dey (3)

(1) Kyungpook National University, N/A, (2) Department of Statistics, Kyungpook National University, N/A, (3) University of Connecticut, N/A

Gyuhyeong Goh  
Department of Statistics, Kyungpook National University

Dipak Dey  
University of Connecticut

Gyeongmin Park  
Kyungpook National University

Gyeongmin Park  
Kyungpook National University

The use of Gibbs sampling for high-dimensional Bayesian regression faces computational challenges due to iterative computation of large-scale covariance matrices. To address this issue, we propose a scalable Bayesian regression framework that incorporates a subsampling strategy into the Gibbs sampling scheme under shrinkage priors including spike-and-slab priors. To correct the bias associated with the sub-sampling method, we employ an acceptance-rejection approach that is scalable to high-dimensional and massive data sets. Our proposed method is applicable to a variety of shrinkage priors that are widely used for high-dimensional Bayesian regression. Our simulation study and real data analysis show that our proposed approach significantly reduces computational costs for Gibbs sampling with high-dimensional and massive data compared to existing scalable MCMC methods.

Acceptance-rejection method|Gibbs sampling|High-dimensional Bayesian regression|Scalable Bayesian computation| |

Section on Bayesian Statistical Science

Bayesian Computation