The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the latter finds fewer applications compared to the former. Hence, this paper initially provides a concise introduction to the theory of the Reject Monte Carlo algorithm and its implementation techniques, aiming to enhance conceptual understanding and program implementation. Subsequently, a simplified rejection Monte Carlo algorithm is formulated. Furthermore, by considering multivariate distribution sampling and multivariate integration as examples, this study explores the specific application of the algorithm in statistical inference.

翻译：蒙特卡洛算法应用日益广泛，其核心步骤涉及从随机模型中进行计算机随机抽样。马尔可夫链蒙特卡洛（MCMC）和拒绝蒙特卡洛均为抽样方法，但后者相较于前者应用较少。因此，本文首先简要介绍拒绝蒙特卡洛算法的理论及其实现技术，旨在加深对概念的理解和程序实现。随后，提出一种简化的拒绝蒙特卡洛算法。此外，以多元分布抽样和多元积分为例，探讨该算法在统计推断中的具体应用。