This paper aims to estimate the lower and upper bounds of the number of accidents that have occurred in the Singapore Strait over the past 10 years on the basis of two maritime accident databases: Global Integrated Shipping Information System and Lloyd's List Intelligence. After an evaluation of the incompleteness of these two databases, a novel and tangible method is proposed to estimate the lower and upper bounds of the number of accidents by using Bayesian analysis under mild assumptions. This method produces the following three important results. First, the annual maritime accident occurrence frequency in the Singapore Strait ranges from 17.6 to 33.0; that is, less than 0.005% of vessels could be involved in an accident when passing through the Strait. Second, the reporting performances of both maritime accident databases to the Singapore Strait are less than 62.5%. In other words, more than 37.5% of maritime accidents are not included in the database. Third, ship collisions account for more than 50% of all types of accidents; this result indicates that a high priority should be assigned to reducing the occurrence of ship collisions by enhancing the navigational systems in the Singapore Strait.