Multisource domain adaptation (MDA) aims to use multiple source datasets with available labels to infer labels on a target dataset without available labels for target supervision. Prior works on MDA in the literature is ad-hoc as the pretraining of source models is either based on weight sharing or uses independently trained models. This work proposes a Bayesian framework for pretraining in MDA by considering that the distributions of different source domains are typically similar. The Hierarchical Bayesian Framework uses similarity between the different source data distributions to optimize the pretraining for MDA. Experiments using the proposed Bayesian framework for MDA show that our framework improves accuracy on recognition tasks for a large benchmark dataset. Performance comparison with state-of-the-art MDA methods on the challenging problem of human action recognition in multi-domain benchmark Daily-DA RGB video shows the proposed Bayesian Framework offers a 17.29% improvement in accuracy when compared to the state-of-the-art methods in the literature.