Ze-HB Hierarchical Bayesian Extension of the Ze

Sequential data prediction presents a fundamental challenge across domains such as genomics and clinical monitoring, demanding approaches that balance predictive accuracy with computational efficiency. This paper introduces Ze, a novel hybrid system that integrates frequency-based counting with hierarchical Bayesian modeling to address the complex demands of sequential pattern recognition. The system employs a dual-processor architecture with complementary forward and inverse processing strategies, enabling comprehensive pattern discovery. At its core, Ze implements a three-layer hierarchical Bayesian framework operating at individual, group, and context levels, facilitating multi-scale pattern recognition while naturally quantifying prediction uncertainty. Implementation results demonstrate that the hierarchical Bayesian approach achieves an 8.3% accuracy improvement over standard Bayesian methods and 2.3× faster convergence through efficient knowledge sharing. The system maintains practical computational efficiency via sophisticated memory management, including automatic counter reset mechanisms that reduce storage requirements by 45%. Ze's modular, open-source design ensures broad applicability across diverse domains, including genomic sequence annotation, clinical time series forecasting, and real-time anomaly detection, representing a significant advancement in sequential data prediction methodology.