So who exactly are these Bayesian Fundamentalists? Since I don’t know or know of any researchers who fit Jones & Love's (J&L's) description, I can’t defend them. Instead, let me describe what my colleagues and students and I have actually done over the last ten years. Some 10 years ago, Clark Glymour and I proposed that children have representations and learning mechanisms that can be characterized as causal models of the world – coherent, structured hypotheses with consistent and predictable relationships to probabilistic patterns of evidence – and that Bayesian inference is one mechanism by which children may learn these models from data.

This proposal has exactly the same status as any other claim in psychology. Since the cognitive revolution, it has been a commonplace that we can explain the mind in terms of representations and rules. It is also a commonplace of the philosophy of cognitive science that these representations and rules can involve many levels of abstraction, from high-level representations such as intuitive theories to neural representations of three-dimensional structure. In vision science, for example, the poster child of successful cognitive science, explanations at many levels from ideal observer theories to neural implementations have been mutually illuminating.

Bayesian learning is just one part of a broader approach, better called the “probabilistic model” approach (see Gopnik & Schulz Reference Gopnik and Schulz2007; Griffiths et al. Reference Griffiths, Chater, Kemp, Perfors and Tenenbaum2010). (For applications to cognitive development, see Gopnik et al. [Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004] and special sections of Developmental Science [Schulz et al. Reference Schulz, Gopnik and Glymour2007b] and Cognition [Buchsbaum et al., in press]). The central advance has not been Bayes’ law itself, but the ability to formulate structured representations, such as causal graphical models, or “Bayes nets” (Pearl Reference Pearl2000; Spirtes et al. Reference Spirtes, Glymour and Scheines2000), or hierarchical causal models, category hierarchies, and grammars, that can be easily combined with probabilistic learning, such as Bayesian inference.

I agree with J&L that formal models are useful only if they can help address empirical questions. For developmental psychologists, the great question is how children can learn as much as they do about the world around them. In the past, “theory theorists” proposed that children learn by constructing hypotheses and testing them against evidence. But if this is a deterministic process, then the “poverty of the stimulus” problem becomes acute. In contrast, if the child is a probabilistic learner, weighing the evidence to strengthen support for one hypothesis over another, we can explain how children are gradually able to revise their initial theories in favor of better ones.

Empirically, we have discovered – as a result of extensive and often challenging experiments – that young children do indeed behave like probabilistic learners, rather than simply using associationist mechanisms to match the patterns in the data or fiddling with details of innate core knowledge. The framework lets us make precise predictions about how children will behave; for example, that they will infer a common cause structure with one set of evidence, but infer a causal chain in an almost identical task with slightly different evidence (Schulz et al. Reference Schulz, Bonawitz and Griffiths2007a). From a more specifically Bayesian perspective, it also allows us to make predictions about the probability of particular responses. The empirical likelihood that a child will make one prediction or another is closely matched to the posterior distribution of hypotheses that support those predictions (e.g., Schulz et al. Reference Schulz, Gopnik and Glymour2007b).

The ultimate test of any perspective is whether it generates new and interesting empirical research. Researchers inspired by this approach have already begun to make important developmental discoveries – discoveries that don’t fit either a connectionist/dynamic or nativist picture. Nine-month-olds, for example, can make causal inferences that go beyond association (Sobel & Kirkham Reference Sobel and Kirkham2006); 20-month-olds can infer a person's desire from a non-random sampling pattern (Kushnir et al. Reference Kushnir, Xu and Wellman2010); and 4-year-olds discover new abstract variables and rules from only a few data points (Lucas et al. Reference Lucas, Gopnik, Griffiths, Ohlsson and Catrambone2010; Schulz et al. Reference Schulz, Goodman, Tenenbaum and Jenkins2008), integrate new evidence and prior knowledge (Kushnir & Gopnik Reference Kushnir and Gopnik2007; Schulz et al. Reference Schulz, Gopnik and Glymour2007b; Sobel et al. Reference Sobel, Tenenbaum and Gopnik2004), and rationally experiment to uncover new causal structure (Schulz & Bonawitz Reference Schulz and Bonawitz2007).

The framework has also enabled us to identify cases where children behave in ways that are interestingly different from ideal inference engines. For example, Kushnir and Gopnik (Reference Kushnir and Gopnik2005) showed that children weight their own actions more heavily than they normatively should for purposes of causal inference. Bonawitz et al. (Reference Bonawitz, Ferranti, Saxe, Gopnik, Meltzoff, Woodward and Schulz2010) have shown that 2-year-olds have difficulty integrating purely correlational information and information about the outcomes of actions.

The precision of these models also enables us to test competing hypotheses. For example, we recently described formal models of learning by imitation. These models gave different weights to statistical evidence and a demonstrator's intentions (Buchsbaum et al., in press). Comparing the models with the data allowed us to show that young children make prior assumptions about why people act, and that these assumptions can explain why they sometimes “overimitate,” reproducing everything that the teacher does, and also predict the degree to which overimitation will occur.

It would certainly be helpful to relate these more abstract accounts to algorithmic-level instantiations. This has already been done to some extent (Danks Reference Danks2003), and we are working on precisely this problem in my lab and others at the moment (Bonawitz et al. Reference Bonawitz, Ferranti, Saxe, Gopnik, Meltzoff, Woodward and Schulz2010). Ultimately, we would also like to relate these representations to neural implementations. It might also be interesting to relate these findings to memory or attention. But this is simply the usual scientific work of connecting different research programs, and we can’t tell which connections will be illuminating beforehand. There is nothing privileged about information processing or neuroscience that means that such research is about “mechanisms” while research into representations is not. This would be like rejecting the explanation that my computer saved the file when I pushed ctrl-s because ctrl-s is the save command in Windows, since this explanation doesn’t refer to the computer's working memory or wiring diagrams.

I would be happy if J&L saw this research program as a part of the Bayesian Enlightenment. If so, however, it is an enlightenment that has been in place for at least ten years.