Infant Statisticians: The Origins of Reasoning Under Uncertainty

Preschoolers use probabilistic evidence to flexibly change or maintain expectations on an active search task

This study investigated 3- to 5-year-olds' (N = 64, 37 girls, 62.5% White, data collected between 2021-2022) ability to use probabilistic information gleaned through active search to appropriately change or maintain expectations. In an online fishing game, children first learned that one of two ponds was good for catching fish. During a subsequent testing phase, children searched the ponds for fish. Half saw outcomes that were probabilistically consistent with training, and the other half saw outcomes that were probabilistically inconsistent. Children in the Inconsistent condition adapted their search strategies, showing evidence of changing their expectations. Those in the Consistent condition maintained their initial search strategy. Trial-by-trial analyses suggested that children used a combination of heuristic and information integration strategies to guide their search behavior.

Probabilistic inference and Bayesian-like estimation in animals: Empirical evidence

Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian-like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian-like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability.

Causal learning by infants and young children: From computational theories to language practices

Causal reasoning-the ability to reason about causal relations between events-is fundamental to understanding how the world works. This paper reviews two prominent theories on early causal learning and offers possibilities for theory bridging. Both theories grow out of computational modeling and have significant areas of overlap while differing in several respects. Explanation-Based Learning (EBL) focuses on young infants' learning about causal concepts of physical objects and events, whereas Bayesian models have been used to describe causal reasoning beyond infancy across various concept domains. Connecting the two models offers a more integrated approach to clarifying the developmental processes in causal reasoning from early infancy through later childhood. We further suggest that everyday language practices offer a promising space for theory bridging. We provide a review of selective work on caregiver-child conversations, in particular, on the use of scaffolding language including causal talk and pedagogical questions. Linking the research on language practices to the two cognitive theories, we point out directions for further research to integrate EBL and Bayesian models and clarify how causal learning unfolds in real life. This article is categorized under: Psychology > Learning Cognitive Biology > Cognitive Development.

Heuristic strategy of intuitive statistical inferences in 7- to 10-year-old children

Intuitive statistical inferences refer to making inferences about uncertain events based on limited probabilistic information, which is crucial for both human and non-human species' survival and reproduction. Previous research found that 7- and 8-year-old children failed in intuitive statistical inference tasks after heuristic strategies had been controlled. However, few studies systematically explored children's heuristic strategies of intuitive statistical inferences and their potential numerical underpinnings. In the current research, Experiment 1 (N = 81) examined 7- to 10-year-olds' use of different types of heuristic strategies; results revealed that children relied more on focusing on the absolute number strategy. Experiment 2 (N = 99) and Experiment 3 (N = 94) added continuous-format stimuli to examine whether 7- and 8-year-olds could make genuine intuitive statistical inferences instead of heuristics. Results revealed that both 7- and 8-year-olds and 9- and 10-year-olds performed better in intuitive statistical inference tasks with continuous-format stimuli, even after focusing on the absolute number strategy had been controlled. The results across the three experiments preliminarily hinted that the ratio processing system might rely on the approximate number system. Future research could clarify what specific numerical processing mechanism may be used and how it might support children's statistical intuitions.

Expecting the Unexpected: Infants Use Others' Surprise to Revise Their Own Expectations

Human infants show systematic responses to events that violate their expectations. Can they also revise these expectations based on others' expressions of surprise? Here we ask whether infants (N = 156, mean = 15.2 months, range: 12.0-18.0 months) can use an experimenter's expression of surprise to revise their own expectations about statistically probable vs. improbable events. An experimenter sampled a ball from a box of red and white balls and briefly displayed either a surprised or an unsurprised expression at the outcome before revealing it to the infant. Following an unsurprised expression, the results were consistent with prior work; infants looked longer at a statistically improbable outcome than a probable outcome. Following a surprised expression, however, this standard pattern disappeared or was even reversed. These results suggest that even before infants can observe the unexpected events themselves, they can use others' surprise to expect the unexpected. Starting early in life, human learners can leverage social information that signals others' prediction error to update their own predictions.

Calculated Feelings: How Children Use Probability to Infer Emotions

Developing the ability to accurately infer others' emotions is crucial for children's cognitive development. Here, we offer a new theoretical perspective on how children develop this ability. We first review recent work showing that with age, children increasingly use probability to infer emotions. We discuss how these findings do not fit with prominent accounts of how children understand emotions, namely the script account and the theory of mind account. We then outline a theory of how probability allows children to infer others' emotions. Specifically, we suggest that probability provides children with information about how much weight to put on alternative outcomes, allowing them to infer emotions by comparing outcomes to counterfactual alternatives.

The language-of-thought as a working hypothesis for developmental cognitive science

A science of prelinguistic infant cognition must take seriously the language-of-thought (LoT) hypothesis. I show how the LoT framework enables us to identify the representational and computational capacities of infant minds and the developmental factors that act on these capacities, and explain how Quilty-Dunn et al.'s take on LoT has important upshots for developmental theory-building.

Three-year-old children's reasoning about possibilities

Recent studies in cognitive development suggest that preschoolers may not be able to represent alternative possibilities, and therefore may lack modal concepts such as possible, impossible, and necessary (Leahy & Carey, 2020). We present two experiments adapted from previous probability studies but have a similar logical structure as those used in the previous modal reasoning tasks (Leahy, 2023; Leahy, Huemer, Steele, Alderete, & Carey, 2022; Mody & Carey, 2016). Three-year-old children have to choose between a gumball machine that must produce the desired gumball color and a gumball machine that merely might produce the desired gumball color. Results provide preliminary evidence that three-year-old children can represent multiple incompatible possibilities, and therefore have modal concepts. Implications for the study of modal cognition, and how possibility and probability may be related are discussed.

Diversity vs. ingroup: How children generalize for the common good

How do children generalize for the common good? The present study investigated whether children are more likely to use the preference of their ingroup (ingroup rationale) or that of a diverse group (diversity rationale) as a basis for generalization about the broader community. In a series of studies, five-year-olds from two different cultures (US and China), yet living in environments with analogous ingroup majority-outgroup minority structure, were asked to generalize either the preference of a diverse sample or the preference of an ingroup sample to the majority. We found that children from both cultures have a default strategy to generalize from their ingroup (Study 1). However, Studies 2-4 show that this ingroup default is amenable to change, suggesting that children mostly use this strategy because ingroup members were salient and conveniently available. When ingroup was removed or reduced (Study 2), or when primed with photos of diverse populations (Studies 3 & 4), children changed their strategies and were more likely to use the diversity-rationale. In both cultures, the intergroup structure of children's living environment exerts similar pressures, resulting in analogous outcomes in generalizing for the common good.

Eristic reasoning: Adaptation to extreme uncertainty

Heuristics (shortcut solution rules) can help adaptation to uncertainty by leading to sufficiently accurate decisions with little information. However, heuristics would fail under extreme uncertainty where information is so scarce that any heuristic would be highly misleading for accuracy-seeking. Thus, under very high levels of uncertainty, decision-makers rely on heuristics to no avail. We posit that eristic reasoning (i.e., self-serving inferences for hedonic pursuits), rather than heuristic reasoning, is adaptive when uncertainty is extreme, as eristic reasoning produces instant hedonic gratifications helpful for coping. Eristic reasoning aims at hedonic gains (e.g., relief from the anxiety of uncertainty) that can be pursued by self-serving inferences. As such, eristic reasoning does not require any information about the environment as it instead gets cues introspectively from bodily signals informing what the organism hedonically needs as shaped by individual differences. We explain how decision-makers can benefit from heuristic vs. eristic reasoning under different levels of uncertainty. As a result, by integrating the outputs of formerly published empirical research and our conceptual discussions pertaining to eristic reasoning, we conceptually criticize the fast-and-frugal heuristics approach, which implies that heuristics are the only means of adapting to uncertainty.

Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny

Humans possess the remarkable capacity to imagine possible worlds and to demarcate possibilities and impossibilities in reasoning. We can think about what might happen in the future and consider what the present would look like had the past turned out differently. We reason about cause and effect, weigh up alternative courses of action and regret our mistakes. In this theme issue, leading experts from across the life sciences provide ground-breaking insights into the proximate questions of how thinking about possibilities works and develops, and the ultimate questions of its adaptive functions and evolutionary history. Together, the contributions delineate neurophysiological, cognitive and social mechanisms involved in mentally simulating possible states of reality; and point to conceptual changes in the understanding of singular and multiple possibilities during human development. The contributions also demonstrate how thinking about possibilities can augment learning, decision-making and judgement, and highlight aspects of the capacity that appear to be shared with non-human animals and aspects that may be uniquely human. Throughout the issue, it becomes clear that many developmental milestones achieved during childhood, and many of the most significant evolutionary and cultural triumphs of the human species, can only be understood with reference to increasingly complex reasoning about possibilities. This article is part of the theme issue 'Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.

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'.

Experiencing statistical information improves children's and adults' inferences

How good are people's statistical intuitions? Recent research has highlighted that sequential experience of statistical information improves adults' statistical intuitions relative to situations where this information is described. Yet little is known about whether this is also the case for children's statistical intuitions. In a study with 100 children (8-11 years old) and 100 adults (19-35 years old), we found that sequentially experiencing statistical information improved both adults' and children's inferences in two paradigmatic reasoning problems: conjunction and Bayesian reasoning problems. Moreover, adults' statistical competencies when they learned statistical information through description were surpassed by children's inferences when they learned through experience. We conclude that experience of statistical information plays a key role in shaping children's reasoning under uncertainty-a conclusion that has important implications for education policy.

Young children’s use of probabilistic reliability and base-rates in decision-making

Children are skilled reasoners who readily use causal, reliability, and base-rate (i.e., prior probability) information in their decisions. Though these abilities are typically studied in isolation, children often must consider multiple pieces of information to make an informed decision. Four experiments (N = 320) explored the development of children’s ability to use reliability and base-rate information when making decisions about draw outcomes. Experiment 1 examined the age at which children can first compare and choose between probabilistically reliable machines. Three- and 4-year-old children saw machines that were probabilistically reliable at obtaining objects while sampling from uniform distributions (i.e., all target or non-target objects). Although 4-year-old children correctly used reliability in their decisions, 3-year-olds did not. In Experiment 2a, 4- to 6-year-olds were presented with the same probabilistically reliable machines, although they sampled from a mixture of target and non-target items. Here, children tended to choose the machine with the better proportion of targets, regardless of reliability. This was replicated in Experiment 2b. In Experiment 3, children were presented with one perfectly reliable machine and one probabilistically unreliable machine. Here, children continued to mostly choose the machine with the better proportion of targets. These results raise questions about base-rate overuse early in development and highlight the need for additional work on children’s ability to use multiple pieces of information in decision-making.

A Model of Scientific Data Reasoning

Data reasoning is an essential component of scientific reasoning, as a component of evidence evaluation. In this paper, we outline a model of scientific data reasoning that describes how data sensemaking underlies data reasoning. Data sensemaking, a relatively automatic process rooted in perceptual mechanisms that summarize large quantities of information in the environment, begins early in development, and is refined with experience, knowledge, and improved strategy use. Summarizing data highlights set properties such as central tendency and variability, and these properties are used to draw inferences from data. However, both data sensemaking and data reasoning are subject to cognitive biases or heuristics that can lead to flawed conclusions. The tools of scientific reasoning, including external representations, scientific hypothesis testing, and drawing probabilistic conclusions, can help reduce the likelihood of such flaws and help improve data reasoning. Although data sensemaking and data reasoning are not supplanted by scientific data reasoning, scientific reasoning skills can be leveraged to improve learning about science and reasoning with data.

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.

Developing an Understanding of Science

Young children are adept at several types of scientific reasoning, yet older children and adults have difficulty mastering formal scientific ideas and practices. Why do “little scientists” often become scientifically illiterate adults? We address this question by examining the role of intuition in learning science, both as a body of knowledge and as a method of inquiry. Intuition supports children's understanding of everyday phenomena but conflicts with their ability to learn physical and biological concepts that defy firsthand observation, such as molecules, forces, genes, and germs. Likewise, intuition supports children's causal learning but provides little guidance on how to navigate higher-order constraints on scientific induction, such as the control of variables or the coordination of theory and data. We characterize the foundations of children's intuitive understanding of the natural world, as well as the conceptual scaffolds needed to bridge these intuitions with formal science.

The elaboration of exploratory play

We apply a new quantitative method for investigating how children's exploration changes across age in order to gain insight into how exploration unfolds over the course of a human life from a life-history perspective. In this study, different facets of exploratory play were quantified using a novel touchscreen environment across a large sample and wide age range of children in the USA (n = 105, ages = 1 year and 10 months to 12 years and 2 months). In contrast with previous theories that have suggested humans transition from more exploratory to less throughout maturation, we see children transition from less broadly exploratory as toddlers to more efficient and broad as adolescents. Our data cast doubt on the picture of human life history as involving a linear transition from more curious in early childhood to less curious with age. Instead, exploration appears to become more elaborate throughout human childhood. This article is part of the theme issue 'Life history and learning: how childhood, caregiving and old age shape cognition and culture in humans and other animals'.

The Acquisition of Modal Concepts

Sometimes we accept propositions, sometimes we reject them, and sometimes we take propositions to be worth considering but not yet established, as merely possible. The result is a complex representation with logical structure. Is the ability to mark propositions as merely possible part of our innate representational toolbox or does it await development, perhaps relying on language acquisition? Several lines of inquiry show that preverbal infants manage possibilities in complex ways, while others find that preschoolers manage possibilities poorly. Here, we discuss how this apparent conflict can be resolved by distinguishing modal representations of possibility, which mark possibility symbolically, from minimal representations of possibility, which do not encode any modal status and need not have a logical structure.