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How can we combine multiple incomplete migration datasets to derive estimates of important migration-related quantities of interest, such as overall migration? Many migration datasets suffer from important omissions or measurement error. Such datasets often exclude specific sub-populations, such as people who migrate informally or people who enter through specific legal categories. This paper presents a Bayesian framework for integrating qualitative knowledge about migration processes with multiple incomplete quantitative datasets to derive more credible estimates of quantities of interests, such as total number of migrants in a given time period or the covariate distribution of a migrant population. The method proves useful for improving upon existing migration measurement tools of digital trace data, geolocation data, demographic surveys, and population registers. The paper applies the toolkit to the Syrian refugee crisis to estimate the scale and characteristics of circular refugee migration from Lebanon to Syria and back.