As scientists, we make rich inferences from sparse, noisy data. These abilities are fundamental not only to inference and discovery in science, but also to the rapid learning that takes place during early childhood. Past research has suggested that children have a robust ability to incorporate their prior knowledge with observed data in order to make causal inferences. But what abilities might support learning when this kind of direct information is not available? In this talk, I will discuss three projects that address different ways in which children can reason about the world even when they have not observed the generative processes that gave rise to the relevant data. First, I will discuss evidence that children and adults have access to metacognitive knowledge about the relative difficulty of discrimination problems, and can use this to determine how much information will be necessary to solve them. Second, I will discuss an ongoing project suggesting that children and adults can infer dynamic causal processes from static scenes. Finally, I will discuss a newly developed project that looks at whether children can infer causal relationships based on abstract, higher order properties of the candidate causes and effects. Taken together, these studies help us to better understand the space of cognitive abilities that support rich inferential reasoning in early childhood.