A Nano-Topological Bayesian Inference Framework for Evaluating Core Hazard Intensity in Clinical Diagnostics

In this this study, we introduced a novel deterministic Coefficient of Intensity derived from nano-topological boundary expansions to isolate the true structural damage caused by symptom removal. Because purely deterministic point-estimates are highly vulnerable to natural sample variance in small data set, we then applied the Bayesian theorem by mapping this coefficient to a Beta-Binomial conjugate model. This Bayesian approach allows us to incorporate statistical uncertainty and generate a posterior distributions that bridge topological approximation with predictive reliability. Statistical hazard intensity is evaluated through Joint Posterior Dominance (computed via Monte Carlo integration) and Interval Displacement (using the Inverse Regularized Beta Function). The proposed Bayesian-Topological model successfully resolves the structural blindness of classical rough set measures. By mathematically filtering out natural sample variance, it proves definitively that Low Platelets is the highly significant driving hazard in Dengue diagnostics. This framework provides a transparent, computationally efficient, and mathematically verified mechanism to rank hazard intensity for clinical decision support and Machine Learning expert systems.