In Bayesian cognitive science, the mind is seen as a spectacular probabilistic-inference machine. But judgment and decision-making (JDM) researchers have spent half a century uncovering how dramatically and systematically people depart from rational norms. In this article, we outline recent research that opens up the possibility of an unexpected reconciliation. The key hypothesis is that the brain neither represents nor calculates with probabilities but approximates probabilistic calculations by drawing samples from memory or mental simulation. Sampling models diverge from perfect probabilistic calculations in ways that capture many classic JDM findings, which offers the hope of an integrated explanation of classic heuristics and biases, including availability, representativeness, and anchoring and adjustment.

Human beings perform well in uncertain environments, matching the performance of complex probabilistic models in complex tasks such as language or physical system prediction. Yet people’s judgments about probabilities also display well-known biases. How can this be? Recently cognitive scientists have explored the possibility that the same sampling algorithms that are used in computer science to approximate complex probabilistic models are also used in the mind and the brain. We the review experimental evidence that characterises the human sampling algorithm, and discuss how such an algorithm could potentially explain apects of the movement of asset prices in financial markets. We also discuss how many of the biases that people display may be the direct result of using only a small number of samples, but using them efficiently. As human beings make successful real-time decisions using only rough estimates of uncertainty, this suggests that machine intelligence could do the same.

Repeated forecasts of changing targets are a key aspect of many everyday tasks, from predicting the weather to financial markets. Random walks provide a particularly simple and informative case study, as new values represent random deviations from the preceding value only, with further previous points being irrelevant. Moreover, random walks often hold simple rational solutions in which predictions should repeat the most recent state, and hence replicate the properties of the target. In previous experiments, however, we have found that human forecasters do not adhere to this standard, showing systematic deviations from the properties of a random walk such as excessive volatility and extreme movements between subsequent predictions. We suggest that such deviations reflect general statistical signatures of human cognition displayed across multiple tasks, offering a window into underlying cognitive mechanisms. Using these deviations as new criteria, we here explore several cognitive models for predicting random walks drawn from various approaches developed in the existing literature, including Bayesian, error-based learning, autoregressive and sampling mechanisms. These models are contrasted to determine which best accounts for the particular statistical features displayed by experimental participants. We find support for sampling models in both aggregate and individual fits, suggesting that these variations are attributable to the use of inherently stochastic prediction systems. We thus argue that variability in predictions is driven by computational noise in the decision making process, rather than ``late'' noise at the output stage.

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