Climate scientists often apply statistical tools to a set of different estimates generated by an “ensemble” of models. In this paper, I argue that the resulting inferences are justified in the same way as any other statistical inference: what must be demonstrated is that the statistical model that licenses the inferences accurately represents the probabilistic relationship between data and target. This view of statistical practice is appropriately termed “model-based,” and I examine the use of statistics in climate fingerprinting to show how the difficulties that climate scientists encounter in applying statistics to ensemble-generated data are the practical difficulties of normal statistical practice. The upshot is that whether the application of statistics to ensemble-generated data yields trustworthy results should be expected to vary from case to case.