Uncertainty without sharing data: federated Bayesian learning

Standard federated Bayesian learning requires agreeing on priors across clients, which is impractical for large models. This work adapts the martingale posterior (predictive Bayes) to the federated setting: clients send only small learned embeddings of their data, and the server recovers parameter uncertainty by repeatedly sampling and refitting. Tests on MNIST, CIFAR-10, and CIFAR-100 show the method matches centralized performance and improves calibration significantly over existing federated approaches.