As a method for operational modal analysis （OMA）， the Bayesian FFT algorithm has garnerd significant attention for its high accuracy and efficiency， as well as its ability of uncertainty quantification. However， different cases of OMA （e.g. well-sep? arated mode， closely-spaced modes， and multi-setup OMA） require different optimization strategy， and it is tedious in computer coding. A new framework is proposed in this paper to unify the above-mentioned cases of OMA， and the implement is simplified as a consequence. Regarding the structural modal response as a latent variable， the single-setup and multi-setup Bayesian OMA is cast as latent variable models， which have been deeply investigated in statistics. An expectation-maximization （EM） algorithm is developed for both single-setup and multi-setup OMA. The introduction of latent variables decouples the parameter optimization in EM， and Louis identity is employed to calculate the Hessian matrix. Two field tests are applied to verify the performance of the proposed approach， with a comparison to the existing algorithm. Consistent results are obtained， and a great advantage in efficiency is observed in the case of closely-spaced modes. The proposed latent variable model unifies the cases of Bayesian OMA， with the advantage of simplified implementation and fast computation. It also paves a way for a further improvement of Bayesian OMA， e.g. with the approach of variational Bayes or Gibbs sampling.