Development of the Bayesian Knowledge Integration Index (BKII): A Quantitative Framework for Assessing Cognitive Integration via Monte Carlo Simulation and Structural Robustness Tests

This conceptual paper introduces the Bayesian Knowledge Integration Index (BKII), a novel metric designed to evaluate the interdisciplinary integration of knowledge in scientific publications. BKII incorporates a detailed hierarchical Bayesian modeling approach with advanced MCMC derivations including detailed mathematical derivations for the NUTS and HMC algorithms, entropy-based information theory, and Rao-Stirling diversity to address citation inflation and closed citation networks. Through Monte Carlo simulations, agent-based modeling, sensitivity analyses, and comparisons with established metrics like the g-index, i10-index, h5-index, CNCI, and implementations like Stan, PyMC, and JAGS, we demonstrate BKII's superior robustness and predictive accuracy under various stress scenarios. The framework is supported by real bibliometric data from OpenAlex, offering a reproducible tool for assessing research impact with implications for academic promotions and funding. No external funding was received, and data are self-contained within the paper.