A Unified Probabilistic Falsifiable Framework (UPFF) for Interdisciplinary Scientific Prediction: Bayesian Hierarchical Modeling, Global Sensitivity Analysis, and Quantitative Falsifiability

This manuscript develops a Unified Probabilistic Falsifiable Framework (UPFF) that combines Bayesian hierarchical modeling, variance-based global sensitivity analysis (Sobol' indices), and a probabilistic reformulation of Popperian falsifiability into a single quantitative workflow for interdisciplinary scientific prediction. The framework defines a closed-form Falsifiability Index (FI) as a normalized Bayes-factor odds ratio, and pairs it with Saltelli-estimator Sobol' sensitivity indices and bootstrap uncertainty quantification. The methodology is demonstrated, with fully reproducible numerical code, on six illustrative applications: a stochastic SIR epidemic model, a zero-dimensional energy-balance climate model, a Bayesian vector-autoregressive macroeconomic model, a one-compartment pharmacokinetic model for vancomycin dosing, a variational Bayesian neural network, and a Bayesian-ridge genomic prediction model. Every quantitative result reported in this manuscript, including posterior means, credible intervals, Sobol' indices with bootstrap confidence bounds, and Falsifiability Indices, is generated by the Python code listed in the Appendix and is reproducible from the manuscript alone. The results are deliberately mixed rather than uniformly favorable. In the epidemiological and macroeconomic applications, the Bayesian posterior-mean forecast offers little or no point-prediction advantage over a well-specified frequentist baseline once a fair comparison is used, so the genuine value of UPFF in those settings lies in calibrated uncertainty quantification rather than raw accuracy. In the pharmacokinetic and genomic-prediction applications, by contrast, where regularization and patient-specific updating address real identifiability and high-dimensionality problems, the Bayesian approach yields large and statistically supported improvements, including a 73 percent reduction in mean AUC prediction error across a simulated 50-patient cohort, with p equal to 8.0 times 10 to the power of negative 8, and a qualitative shift from negative to positive out-of-sample R squared under conditions where the number of predictors exceeds the number of observations. We report these mixed, sometimes null, results transparently, discuss the framework's limitations, and provide a dedicated Scientific and Technical Risk Assessment together with a Roadmap, Experimental Validation, and Falsifiability section that specifies, for each application domain, the concrete observations that would corroborate or refute the framework's central claims.