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Personalized federated learning (PFL) based on Bayesian approach tackle the challenges from statistical heterogeneity of client data by computing a personalized posterior distribution over the parameters of each client's local model and constructing a global distribution by aggregating the parameters of these personalized posteriors. However, the heuristic aggregation methods introduce strong biases and result in global models with poor generalization. We thus propose a novel hierarchical Bayesian inference framework for PFL by specifying a conjugate hyper-prior over the parameters of the personalized posteriors. This allows us to jointly compute a global posterior distribution for aggregation and the personalized ones at local level. This hierarchical Bayesian inference framework achieves elegant balance between local personalization and global model robustness. Extensive empirical study shows that by effectively sharing the heterogeneous statistical strength across the local models while retaining their distinctive characteristics, our framework yields state-of-the-art performance. We also show that existing Bayesian PFLs are special cases of our framework.