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Conventional detectors in tracking system generally work according to the Neyman-Pearson criterion. Recently, Bayesian detection has become an alternative for many trackers such as probabilistic data association filter (PDAF). However, a critical problem of the tracking system with Bayesian detection is to predict the tracking performance without simulations. As the Bayesian detection is introduced, clutters are nonuniformly distributed and the detection threshold varies with time, which increases the difficulty of the analysis. In this paper, an offline method is developed to predict the performance of the PDAF with Bayesian detection (PDAF-BD). In the approach, the information reduction factor (IRF) of the PDAF-BD is derived, describing the influence of measurement origin uncertainty. Unlike the IRF of PDAF, the IRF of PDAF-BD has analytical expression which is efficient in computation. On this basis, the offline recursion of the error covariance and the quantification of track loss are achieved. The experiments show that the nonsimulated result generated by the proposed algorithm is reasonably close to the simulated one.