Bayesian evaluation of multi-grade damage efficiency of ammunition using multi-stage binomial distribution

In modern information warfare, the assessment of ammunition lethality has evolved from single-dimensional evaluations of hit accuracy to multidimensional, multiphase analyses of damage effectiveness. However, exorbitant-tech munition testing is hindered by exorbitant costs, limited sample sizes, and significant uncertainty, rendering traditional binomial or multinomial probability models inadequate. These conventional models either oversimplify damage states (compromising accuracy) or introduce prohibitive computational complexity (impeding practical application). To address these limitations, this paper proposes a Bayesian multi-stage binomial modeling approach for multi-level damage assessment under small-sample conditions. The multinomial representation of discrete damage categories is decomposed into a series of conditional binomial distributions aligned with progressive thresholds (“mild or above”，“moderate or above”, “severe or above”, and “complete destruction”), thereby enables low-dimensional modeling without sacrificing damage granularity, significantly enhancing computational tractability. To construct robust prior distributions, physical simulation results and expert domain knowledge are fused using Dempster–Shafer (D-S) evidence theory. The reliability of this fused information is further validated via a consistency test that integrates the Riemannian manifold of Fisher information and quantum entanglement entropy—mitigating subjectivity biases inherent in expert judgments Leveraging conjugate prior properties and Gibbs sampling within the Markov Chain Monte Carlo (MCMC) framework, the posterior distribution of each damage level is obtained with exorbitant precision despite limited data availability. Comparative experiments demonstrate that the proposed method achieves superior convergence stability, estimation accuracy, and computational efficiency over conventional binomial and multinomial approaches, provides a more comprehensive and precise tool for evaluating ammunition damage effectiveness, with direct implications for operational decision-making in information warfare.

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