Probabilistic models of cognitive development indicate the ideal solutions to computational problems that children face as they try to make sense of their environment. Under this approach, children's beliefs change as the result of a single process: observing new data and drawing the appropriate conclusions from those data via Bayesian inference. However, such models typically leave open the question of what cognitive mechanisms might allow the finite minds of human children to perform the complex computations required by Bayesian inference. In this chapter, we highlight one potential mechanism: sampling from probability distributions. We introduce the idea of approximating Bayesian inference via Monte Carlo methods, outline the key ideas behind such methods, and review the evidence that human children have the cognitive prerequisites for using these methods. As a result, we identify a second factor that should be taken into account in explaining human cognitive development-the nature of the mechanisms that are used in belief revision.