In many situations human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and that predicted by Bayesian inference: people often appear to make judgments based on a few samples from a probability distribution, rather than the full distribution. Although sample-based approximations are a common implementation of Bayesian inference, the very limited number of samples used by humans seems to be insufficient to approximate the required probability distributions. Here we consider this discrepancy in the broader framework of statistical decision theory, and ask: if people were making decisions based on samples, but samples were costly, how many samples should people use? We find that under reasonable assumptions about how long it takes to produce a sample, locally suboptimal decisions based on few samples are globally optimal. These results reconcile a large body of work showing sampling, or probability-matching, behavior with the hypothesis that human cognition is well described as Bayesian inference, and suggest promising future directions for studies of resource-constrained cognition.

The literature on concept development is highly contentious because there is a lot at stake. The processes that give rise to categories are at the very core of how we understand human cognition. In broad strokes, the debate is about whether categories reflect internal representations that are highly stable symbolic proposition-like and manipulated via logical operators or, whether they are probabilistic, context-dependent, and derived from bundles of correlated features and ordinary processes of perceiving and remembering (for reviews, see, Komatsu, 1992; Murphy & Medin, 1989; E. Smith, 1989; E. Smith & Medin, 1981. The literature appears to cycle through these two classes of accounts, advancing with each pass through but never quite leaving these two general points of view. Many of the contentious issues in the developmental literature on concepts and categories are variants of this debate. Accordingly, this review begins with a brief history of theories of categories. This is as history of back-and-forth transitions between a focus on more the more stable and the more probabilistic aspects of categories and it is a debate that is not resolved. However, by either view, categories result from internal representations that capture the structure in the world. Accordingly, the review of the developmental literature is organized with respect to recent advances in understanding outside-the-mind factors that organize and recruit the cognitive processes that create categories: the statistical regularities in the learning environment, the cognitive tasks and the nested time scales of the internal processes they recruit, and the body which is the interface between the external world and cognition. Back – and – forth theories. 2 Traditionally, categories are viewed as discrete bounded things that are stable over time and context. In this view, categories are enduringly real, object-like, truly out there in the world and also in our heads. Thus, theorists in this tradition write about categories being acquired, discovered, and possessed. The boundedness and stability expected of categories is well exemplified in the following quote from Keil (1994): Shared mental structures are assumed to be constant across repeated categorizations of the same set of instances and different from other categorizations. When I think

doi: 10.3389/fnhum.2011.00039 A Bayesian foundation for individual learning under uncertainty

In everyday word learning words are only sometimes heard in the presence of their referent, making the acquisition of novel words a particularly challenging task. The current study investigated whether children (18-month-olds who are novice word learners) can track the statistics of co-occurrence between words and objects to learn novel mappings in a stochastic environment. Infants were briefly trained on novel word–novel object pairs with variable degrees of co-occurrence: Words were either paired reliably with 1 referent or stochastically paired with 2 different referents with varying probabilities. Infants were sensitive to the co-occurrence statistics between words and referents, tracking not just the strongest available contingency but also low-frequency information. The statistical strength of the word–referent mapping may also modulate real-time online lexical processing in infants. Infants are thus able to track stochastic relationships between words and referents in the process of learning novel words.

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the what, the how, and the why of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for developmentalists. We emphasize a qualitative understanding of Bayesian inference, but also include information about additional resources for those interested in the cognitive science applications, mathematical foundations, or machine learning details in more depth. In addition, we discuss some important interpretation issues that often arise when evaluating Bayesian models in cognitive science.