Reliable inference requires that artificial intelligence (AI) models provide trustworthy uncertainty estimates, not merely accurate predictions. Recent advances in Bayesian learning have made significant progress toward this goal, and growing concerns about computational overhead have jointly shifted the design criterion from reliability alone to the co-design of reliability and efficiency, i.e., reducing computational overhead while preserving trustworthy uncertainty quantification. This thesis develops a unified framework from two perspectives to address the central question: can we efficiently perform reliable inference?