When Mr. Blicket Wants It, Children Are Bayesian

When Mr. Blicket Wants It, Children are Bayesian David M. Sobel (Sobel@cog.brown.edu) Department of Cognitive and Linguistic Sciences, Box 1978, Brown University Providence, RI, 02912 USA Sarah Munro (Sarah.Munro@ubc.ca) Department of Psychiatry, University of British Columbia, 2255 Wesbrook Mall Vancouver, BC, V6T 2A1 Canada children to a “blicket detector”: a machine that lights up and plays music when certain objects (controlled by the experimenter) are placed upon it. They used a device that presented a novel causal property of objects to children to control what prior knowledge the child brought to the learning environment. They told children that “Blickets make the machine go”, and initially trained them that the base rate of blickets in the world was either rare or common. They placed 12 identical objects on the machine one at a time, and either 2 or 10 of those objects activated it (and were categorized as blickets). They then presented children with ambiguous data: a backwards blocking procedure in which they took two new identical objects (A and B) and placed them on the detector together, which activated, and then placed only object A on the machine alone, which also activated. Object A is clearly a blicket, but object’s B’s “blicketness” is uncertain. If children responded on the basis of the prior probability of blickets, then when blickets are rare, they should say B is not a blicket, but when blickets are common, they should say B is a blicket. This was the pattern of performance observed in 4-year-olds, but not younger children: Three-year-olds categorized object B as a blicket in both conditions. This procedure has been replicated and extended to other empirical paradigms that test Bayesian inference more explicitly (e.g., Tenenbaum et al., submitted). At issue here is whether children are developing a mechanism best described by Bayesian inference between ages 3 and 4, or if 3-year-olds possess such a mechanism and lack other pieces of substantive prior knowledge necessary to use it. One way of considering this question is to examine what substantive knowledge children must possess in order to form a hypothesis space about blickets and blicket detectors. Following Tenenbaum & Griffiths (2003), Sobel et al. (2004) posited that children must have several pieces of information in order to form an accurate and representative hypothesis space. They must recognize that there are two types of objects in the world: objects and detectors. Objects are placed on detectors, and detectors either activate or not. Three- and 4-year-olds appear to have this knowledge. Next, children must recognize the temporal relationship between objects and the detector activating. Namely, that placing an object on the detector causes it to activate, not that the detector activating causes the experimenter to place an object on it. Similarly, children must recognize that there is some form of spatial independence among the objects. Abstract Sobel, Tenenbaum, and Gopnik (2004) demonstrated that 4- year-olds’ but not 3-year-olds’ causal inferences were well- described by a Bayesian mechanism that relies on specific causal knowledge. Sobel et al. (submitted) demonstrated that this causal knowledge developed between ages 3-4, suggesting that if 3-year-olds had access to this knowledge, their inferences could also be described by this Bayesian mechanism. These experiments all used a “blicket detector”, which presented a novel causal property of objects. But this procedure was limited to children’s understanding of physical causality. Here, we demonstrated that 3-year-olds have this requisite causal knowledge when the causal relations are presented in the psychological domain (specifically an agent’s desire), and given this finding, then demonstrated that 3-year- olds’ causal inferences about another’s desires are well- described by this Bayesian mechanism. Bayesian Causal Inference Researchers in cognitive development have suggested that young children possess causal knowledge across the physical (e.g., Leslie & Keeble, 1987), psychological (e.g., Gopnik & Wellman, 1994), and biological (e.g., Kalish, 1996) domains. There is much consensus on children possessing causal knowledge – even in infancy – but there is little agreement on how that causal knowledge is represented or learned. Several researchers have recently appealed to causal graphical models as a way of representing children’s causal knowledge (e.g., Gopnik, Glymour, Sobel, et al., 2004). Some researchers have appealed to Bayesian inference over a hypothesis space of these graphical models as a description of how children learn new causal relations and engage in causal inference (e.g., Sobel, Tenenbaum, & Gopnik, 2004). Under this Bayesian approach, learners use the substantive prior knowledge available to them to form a hypothesis space of causal models that potentially generated the observed data. Those hypotheses are each assigned a prior probability of being the correct hypothesis. Data are observed, and those hypotheses are updated via an application of Bayes’ theorem (see Tenenbaum et al., submitted, for a more formal description of this algorithm). What this approach suggests is that ambiguous data observed in the world can be resolved by appealing to the initial prior probabilities that hypotheses were assigned. Sobel et al. (2004) tested this prediction by introducing