Expectations about single event probabilities in the first year of life: The influence of perceptual and statistical information

The pupillometry of the possible: an investigation of infants' representation of alternative possibilities

Contrasting possibilities has a fundamental adaptive value for prediction and learning. Developmental research, however, has yielded controversial findings. Some data suggest that preschoolers might have trouble in planning actions that take into account mutually exclusive possibilities, while other studies revealed an early understanding of alternative future outcomes based on infants' looking behaviour. To better understand the origin of such abilities, here we use pupil dilation as a potential indicator of infants' representation of possibilities. Ten- and 14-month-olds were engaged in an object-identification task by watching video animations where three different objects with identical top parts moved behind two screens. Importantly, a target object emerged from one of the screens but remained in partial occlusion, revealing only its top part, which was compatible with a varying number of possible identities. Just as adults' pupil diameter grows monotonically with the amount of information held in memory, we expected that infants' pupil size would increase with the number of alternatives sustained in memory as candidate identities for the partially occluded object. We found that pupil diameter increased with the object's potential identities in 14- but not in 10-month-olds. We discuss the implications of these results for the foundation of humans' capacities to represent alternatives. This article is part of the theme issue 'Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.

A description-experience gap in statistical intuitions: Of smart babies, risk-savvy chimps, intuitive statisticians, and stupid grown-ups

Comparison of different lines of research on statistical intuitions and probabilistic reasoning reveals several puzzling contradictions. Whereas babies seem to be intuitive statisticians, surprisingly capable of statistical learning and inference, adults' statistical inferences have been found to be inconsistent with the rules of probability theory and statistics. Whereas researchers in the 1960s concluded that people's probability updating is "conservatively" proportional to normative predictions, probability updating research in the 1970s suggested that people are incapable of following Bayes's rule. And whereas animals appear to be strikingly risk savvy, humans often seem "irrational" when dealing with probabilistic information. Drawing on research on the description-experience gap in risky choice, we integrate and systematize these findings from disparate fields of inquiry that have, to date, operated largely in parallel. Our synthesis shows that a key factor in understanding inconsistencies in statistical intuitions research is whether probabilistic inferences are based on symbolic, abstract descriptions or on the direct experience of statistical information. We delineate this view from other conceptual accounts, consider potential mechanisms by which attributes of first-hand experience can facilitate appropriate statistical inference, and identify conditions under which they improve or impair probabilistic reasoning. To capture the full scope of human statistical intuition, we conclude, research on probabilistic reasoning across the lifespan, across species, and across research traditions must bear in mind that experience and symbolic description of the world may engage systematically distinct cognitive processes.

Infant Statisticians: The Origins of Reasoning Under Uncertainty

Humans frequently make inferences about uncertain future events with limited data. A growing body of work suggests that infants and other primates make surprisingly sophisticated inferences under uncertainty. First, we ask what underlying cognitive mechanisms allow young learners to make such sophisticated inferences under uncertainty. We outline three possibilities, the logic, probabilistic, and heuristics views, and assess the empirical evidence for each. We argue that the weight of the empirical work favors the probabilistic view, in which early reasoning under uncertainty is grounded in inferences about the relationship between samples and populations as opposed to being grounded in simple heuristics. Second, we discuss the apparent contradiction between this early-emerging sensitivity to probabilities with the decades of literature suggesting that adults show limited use of base-rate and sampling principles in their inductive inferences. Third, we ask how these early inductive abilities can be harnessed for improving later mathematics education and inductive inference. We make several suggestions for future empirical work that should go a long way in addressing the many remaining open questions in this growing research area.

Infants Distinguish Between Two Events Based on Their Relative Likelihood

Likelihood estimations are crucial for dealing with the uncertainty of life. Here, infants' sensitivity to the difference in likelihood between two events was investigated. Infants aged 6, 12, and 18 months (N = 75) were shown animated movies of a machine simultaneously drawing likely and unlikely samples from a box filled with different colored balls. In different trials, the difference in likelihood between the two samples was manipulated. The infants' looking patterns varied as a function of the magnitude of the difference in likelihood and were modulated by the number of items in the samples. Looking patterns showed qualitative similarities across age groups. This study demonstrates that infants' looking responses are sensitive to the magnitude of the difference in likelihood between two events.

Infants' Looking to Surprising Events: When Eye-Tracking Reveals More than Looking Time

Research on infants' reasoning abilities often rely on looking times, which are longer to surprising and unexpected visual scenes compared to unsurprising and expected ones. Few researchers have examined more precise visual scanning patterns in these scenes, and so, here, we recorded 8- to 11-month-olds' gaze with an eye tracker as we presented a sampling event whose outcome was either surprising, neutral, or unsurprising: A red (or yellow) ball was drawn from one of three visible containers populated 0%, 50%, or 100% with identically colored balls. When measuring looking time to the whole scene, infants were insensitive to the likelihood of the sampling event, replicating failures in similar paradigms. Nevertheless, a new analysis of visual scanning showed that infants did spend more time fixating specific areas-of-interest as a function of the event likelihood. The drawn ball and its associated container attracted more looking than the other containers in the 0% condition, but this pattern was weaker in the 50% condition, and even less strong in the 100% condition. Results suggest that measuring where infants look may be more sensitive than simply how much looking there is to the whole scene. The advantages of eye tracking measures over traditional looking measures are discussed.