Bayesian Transfer Learning for Enhanced Estimation and Inference

Transfer learning enhances model performance in a target population with limited samples by leveraging knowledge from related studies. While many works focus on improving predictive performance, challenges persist in statistical inference. Bayesian approaches naturally provide uncertainty quantification for parameter estimates; however, existing Bayesian transfer learning methods are typically limited to single-source scenarios or require individual-level data. We introduce TRansfer leArning via guideD horseshoE prioR (TRADER), a novel approach enabling multi-source transfer through pre-trained models in high-dimensional linear regression. TRADER shrinks target parameters toward an adaptively weighted average of source estimates, while remaining robust to differences in source scale and correlation. Theoretical investigation shows that TRADER achieves faster posterior contraction rates than standard continuous shrinkage priors when sources are well-aligned with the target, while preventing negative transfer from heterogeneous sources. The finite-sample marginal posterior behavior of TRADER is established. Extensive simulations show that TRADER achieves inference performance no worse than using target data alone, performs comparably to a competing frequentist method despite using only summary-level source data, and offers substantial computational advantages. Application to a high-dimensional genetic dataset further shows TRADER's effectiveness in inference under strong multicollinearity. Supplementary materials for this article, including a standardized reproducibility guide detailing all materials required to replicate the results, are available online.