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.
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