This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support Vector Machines (SVM). Utilizing ensemble methods, represented by the equation yensemble = M ∈M wM · yM , and stacking techniques, the study formulates a unique hybrid predictive system. The research rigorously explores the properties of individual non-Bayesian models, establishing their feature importance , generalization error, and optimization landscapes through lemmas and theorems. It proves the optimality of the proposed ensemble method and the robustness of the stacking technique. Feature integration is mathematically formulated to achieve significant information gain. Additionally, in synthesizing the findings, our research corroborates the mathematical formulations underlying ensemble methods while offering nuanced insights into the limitations of hyperparameter tuning. Specifically, the ensemble method empirically validates the ensemble generalization error equation Eensemble = n i=1 w 2 i ϵi + 2 n i=1 j̸ =i wiwjρ(Mi, Mj)ϵiϵj, showcasing the ensemble’s minimized generalization error. This is further optimized through the Lagrangian function L(w1, w2,. .. , wn, λ) = Eensemble + λ 1 − n i=1 wi , allowing for adaptive weight adjustments. Feature integration solidifies these results by emphasizing the second-order conditions for optimality, including stationarity (∇L = 0) and positive definiteness of the Hessian matrix. Conversely, hyperparameter tuning indicates a subdued impact in improving Expected Improvement (EI), represented by EI(x) = E[max(f (x) − f (x *), 0)]. Overall, the ensemble method stands out as a robust, algorithmically optimized approach.