(untitled) (International Journal of Latest Technology in Engineering Management & Applied Science, 2025)
Background: University administrators encounter multi-faceted decision-making problems including resource distribution, prediction of incoming enrollments and optimization of student success in the face of underlying uncertainty. The traditional deterministic models can hardly represent dynamic interdependence of educational systems. Methods: Authors present a holistic Bayesian statistical tool of university management, with hierarchical Bayesian and Bayesian optimization tools and Markov Chain Monte Carlo (MCMC) tools. Combining both the previous institutional knowledge and the observed data to give strong uncertainty quantification to administrative choices. Results: Simulation experiments and empirical research indicate that predictive performance is better than frequentist methods by 15-20% in the accuracy of enrollment prediction and a substantial increase in resource allocation efficiency. Bayesian model offers Confidential intervals that can be easily interpreted and high adaptability in decision making. Conclusions: Bayesian techniques provide a principled management tool to university administration, allowing data-driven decisions and clearly defining uncertainty. It helps in fair allocation of resources and enhance institutional strength in changing learning conditions.