In recent years, public administration experiments and their replication have become an important way to improve the generalizability of theories. However, experimental replication still faces a series of methodological issues that need to be addressed: how to effectively establish the relevance and comparability of replication with the original study? How to design and analyze replication experiments reasonably and allow for flexible adjustments? How to optimize the design to reduce sample size and cost, and to improve efficiency and effectiveness? This paper proposes a design framework based on Bayesian Experiments to provide a more adaptive path for replication of public administration experiments. Unlike Randomized Controlled Trials (RCTs) based on Frequency Statistics, Bayesian Experiments can, first, take background knowledge such as original research as priors and perform Bayesian updating based on data and likelihood functions. Second, the use of posterior probabilities instead of using P-values to test research hypotheses avoids problems such as P-hacking. In a sequential setting, subsequent designs can be quickly adjusted based on previous results, while ensuring comparability of results across experimental arms. It is also possible to determine the location, context, and sample for further experimental replication based on structural speculation. Finally, Bayesian experiments can be used to transform the intervention maximization problem into a "multi-armed bandit problem" in reinforcement learning by using algorithms such as as Thompson sampling to deterministically assign subjects, it could significantly reduce the sample size and experimental cost, and has a wide range of application prospects.