In view of the small sample size of combat ammunition trial data and the difficulty of forecasting the demand for combat ammunition, a Bayesian inference method based on multinomial distribution is proposed. Firstly, considering the different damage grades of ammunition hitting targets, the damage results are approximated as multinomial distribution, and a Bayesian inference model of ammunition demand based on multinomial distribution is established, which provides a theoretical basis for forecasting the ammunition demand of multigrade damage under the condition of small samples. Secondly, the conjugate Dirichlet distribution of multinomial distribution is selected as a prior distribution, and Dempster–Shafer evidence theory (D-S theory) is introduced to fuse multisource previous information. Bayesian inference is made through the Markov chain Monte Carlo method based on Gibbs sampling, and ammunition demand at different damage grades is obtained by referring to cumulative damage probability. The study result shows that the Bayesian inference method based on multinomial distribution is highly maneuverable and can be used to predict ammunition demand of different damage grades under the condition of small samples.

中文翻译：

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基于多项式分布的弹药需求贝叶斯估计

鉴于作战弹药试验数据样本量少，难以预测作战弹药需求，提出了一种基于多项式分布的贝叶斯推理方法。首先，考虑弹药打击目标的不同伤害等级，将伤害结果近似为多项式分布，建立了基于多项式分布的弹药需求贝叶斯推断模型，为预测多种弹药对弹药的弹药需求提供了理论基础。小样品的状况。其次，选择多项式分布的共轭Dirichlet分布作为先验分布，并引入Dempster-Shafer证据理论（DS理论）融合多源先验信息。贝叶斯推断是通过基于吉布斯采样的马尔可夫链蒙特卡罗方法进行的，并通过累积损伤概率来获得不同损伤等级下的弹药需求。研究结果表明，基于多项式分布的贝叶斯推理方法具有很高的可操作性，可用于在小样本情况下预测不同损伤等级的弹药需求。