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Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should combine prior knowledge with observed data. Comparing this model with human judgments provides constraints on possible algorithms that people might use to predict the future. In the experiments, we examine the effects of multiple observations, the effects of prior knowledge, and the difference between independent and dependent observations, using both descriptions and direct experience of prediction problems. The results indicate that people integrate prior knowledge and observed data in a way that is consistent with our Bayesian model, ruling out some simple heuristics for predicting the future. We suggest some mechanisms that might lead to more complete algorithmic-level accounts.