Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cellular migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we develop a probabilistic, hierarchical framework. This framework provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine drawing reliable conclusions - uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both discrete and continuous process models are considered and related via hierarchical conditional probability assumptions. This allows the incorporation of features of both continuum tissue models and discrete cellular models. We perform model checks on both in-sample and out-of-sample datasets and use these checks to illustrate how to test possible model improvements and assess the robustness of our conclusions. This allows us to consider - and ultimately decide against - the need to retain finite-cell-size effects to explain a small misfit appearing in one set of long-time, out-of-sample predictions. Our approach leads us to conclude, for the present set of experiments, that a primarily proliferation-driven model is adequate for predictions over most time-scales. We describe each stage of our framework in detail, and hope that the present work may also serve as a guide for other applications of the hierarchical approach to problems in computational biology.