A Generalized Multi-Stage Conditional Probability Inference Framework with Heterogeneous Information Fusion

In complex system evaluation and decision-making under uncertainty, accurately assessing multi-level performance states using small-sample data remains a fundamental challenge. To address this gap, this paper proposes the novel, generalized Bayesian inference framework built upon the mul-ti-stage conditional probability model. Concurrently, the system contribution degree is introduced as the weight for Bayesian fusion. The Gibbs sampling MCMC algorithm is adopted for posterior inference, with strict sequential constraints established to validate performance improvements across successive batches. The effectiveness of the proposed method under small-sample scenarios is verified through multiple batches of performance enhancement tests conducted during the iterative development of the key strategic material. Results demonstrate that this framework more accurately and stably captures the evolutionary trend of material performance, offering the scien-tific, systematic, and universally applicable solution for multi-batch performance evaluation with small samples.