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Vertical deflection has been emphasized as an important safety indicator in the management of railway bridges. Therefore, various standards and studies have suggested physics-based models for predicting the time-dependent deflection of railway bridges. However, these approaches may be limited by model errors caused by uncertainties in various factors, such as material properties, creep coefficient, and temperature. This study proposes a new Bayesian method that employs both a finite element model and actual measurement data. To overcome the limitations of an imperfect finite element model and a shortage of data, Gaussian process regression is introduced and modified to consider both, the finite element analysis results and actual measurement data. In addition, the probabilistic prediction model can be updated whenever additional measurement data is available. In this manner, a probabilistic prediction model, that is customized to a target bridge, can be obtained. The proposed method is applied to a pre-stressed concrete railway bridge in the construction stage in the Republic of Korea, as an example of a bridge for which accurate time-dependent deflection is difficult to predict, and measurement data are insufficient. Probabilistic prediction models are successfully derived by applying the proposed method, and the corresponding prediction results agree with the actual measurements, even though the bridge experienced large downward deflections during the construction stage. In addition, the practical uses of the prediction models are discussed. [ABSTRACT FROM AUTHOR]