AbstractThis chapter focuses on the broad methodological and philosophical underpinnings of the Bayesian model-based approach to studying migration. Starting from reflections on the uncertainty and complexity in demography and, in particular, migration studies, the focus moves to the shifting role of formal modelling, from merely describing, to predicting and explaining population processes. Of particular importance are the gaps in understanding asylum migration flows, which are some of the least predictable while at the same time most consequential forms of human mobility. The well-recognised theoretical void of demography as a discipline does not help, especially given the lack of empirical micro-foundations in formal modelling. Here, we analyse possible solutions to theoretical shortcomings of demography and migration studies from the point of view of the philosophy of science, looking at the inductive, deductive and abductive approaches to scientific reasoning. In that spirit, the final section introduces and extends a research programme of model-based demography.