Model-based offline multi-agent reinforcement learning (MARL) provides a promising approach to multi-agent decision-making under partial observability, where the global state is unavailable from offline data. However, limited dataset coverage can lead to substantial out-of-distribution (OOD) model errors, which may mislead policy optimization and degrade downstream performance. Existing model-based offline MARL methods typically rely on access to global states or mitigate model errors through pessimistic or conservative policy optimization, leaving the reliability and refinement of learned world models less explored. We propose a Bayesian offline MARL framework that infers latent global states from decentralized observation-action histories and iteratively refines a posterior world model using only offline data. Building on posterior information loss, we extend this criterion to the multi-agent setting as multi-agent posterior information loss (MPIL), which provides a reliability measure for world model refinement and offline evaluation. Theoretically, we establish an upper bound on policy regret that is monotonic in MPIL and further characterize its dependence on the size and state-joint-action coverage of the offline dataset. Experiments on partially observable multi-agent variants of D4RL MuJoCo tasks demonstrate competitive policy performance across diverse offline data conditions, while MPIL-guided refinement improves world model prediction and downstream policy performance. These results support a principled connection between world model reliability, offline data coverage, and policy performance in partially observable offline MARL.

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