The target article by Jones & Love (J&L) is timely, given the growing importance of Bayesian models and the need to assess these models by the same standards applied to other models of cognition. J&L's comments about the pitfalls of behaviorism as well as connectionist modeling are well made and give good reason to be cautious in the development of Bayesian models. Likewise, the comments about recent trends in economics pose an interesting challenge for Bayesian modeling.

However, the religious metaphor is not apt. Most researchers cited under the heading of Bayesian Fundamentalism also have interests in psychological mechanisms and/or neural implementation and employ other modeling approaches in addition to Bayesian modeling. Hence, Bayesian modeling is less of a new religion and more of a new tool for researchers who study cognition by using both empirical and modeling methods (cf. Lewandowsky & Heit Reference Lewandowsky and Heit2006). Although there is merit to J&L's point that Bayesian modeling often does not include empirical measurement of the environment, it would be a mistake to say that Bayesian modeling is mainly a normative approach or that it does not involve data collection. Most Bayesian research cited by J&L considers the adequacy of Bayesian models as descriptive models and compares their predictions to human data.

Therefore, we would say that Bayesians are just like everyone else. Bayesian models are often very similar, if not equivalent, to other kinds of models. For example, in memory research, a biologically inspired connectionist model (Norman & O’Reilly Reference Norman and O'Reilly2003) makes many of the same predictions as earlier Bayesian models of memory (McClelland & Chappell Reference McClelland and Chappell1998; Shiffrin & Steyvers Reference Shiffrin and Steyvers1997). In this case, the Bayesian models fit a large number of results and could no more be dismissed on the basis of experimental data than connectionist models. Indeed, connectionist models can implement approximate Bayesian inference (McClelland Reference McClelland, Oaksford and Chater1998), and exemplar models likewise have this capability (Heit Reference Heit, Moore and Lehman1995; Shi et al. Reference Shi, Griffiths, Feldman and Sanborn2010). At a more general level, connectionist models such as mixture of experts models (Heit & Bott Reference Heit, Bott and Medin2000; Heit et al. Reference Heit, Briggs and Bott2004; Jacobs Reference Jacobs1997), as well as exemplar models (Heit Reference Heit, Hahn and Ramscar2001), can implement the key notion of Bayesian models – that prior knowledge is integrated with new observations to form a posterior judgment. Thus, it is difficult to dismiss Bayesian models when alternative models are fundamentally doing the same work or even making the same predictions.

J&L do not place sufficient weight on one of the main benefits of Bayesian models; namely, in explaining how prior hypotheses are put together with new observations. Cognitive activities take place in knowledge- and meaning-rich environments; for example, expectations, stereotypes, and theories affect memory, reasoning, and categorization (e.g., Bartlett Reference Bartlett1932; Dube et al. Reference Dube, Rotello and Heit2010; Hayes et al. Reference Hayes, Heit and Swendsen2010; Heit Reference Heit, Lamberts and Shanks1997; Heit & Bott Reference Heit, Bott and Medin2000; Murphy & Medin Reference Murphy and Medin1985). The role of knowledge is often obscured in experimental research using abstract stimuli. It would be a sterile model of cognition indeed that could only deal with these blank-slate situations involving meaningless materials. The approach of Bayesian models, incorporating prior hypotheses, is crucial to their success as models of many cognitive activities, and is a distinctive advantage over models that assume cognition does not incorporate prior hypotheses.

The target article criticizes Bayesian models for a lack of representational assumptions. This point is questionable; hypothesis spaces are arguably representations of the world and could be treated as psychological representations (Heit Reference Heit, Oaksford and Chater1998; Reference Heit2000; Kemp & Tenenbaum Reference Kemp and Tenenbaum2009). However, a lack of representational assumptions could be a virtue, because representational assumptions are usually wrong, or at best, untestable. For example, in reasoning research, there has been a long-running debate between mental model representation and mental rule representation; in categorization research, there has been a related debate between exemplar representation versus abstract representation (Rips Reference Rips1990). Presumably, in each case at least one assumed form of representation is wrong, although decades of research has not resolved the matter. It has been further argued that sufficiently powerful representational systems, along with appropriate processing assumptions, are indistinguishable (Anderson Reference Anderson1978; Barsalou Reference Barsalou, Srull and Wyer1990). On these grounds, any lack of strong representational assumptions in Bayesian models seems a wise approach.

A similar point can be made about a lack of predictions for the neural level. Not making predictions about the brain could actually be a virtue, if the alternative is to force post hoc predictions that do not follow distinctively from the model. For example, the mental model theory of reasoning has often been tested by looking for activation in the left hemisphere of the brain. The origin of this prediction appears to be Johnson-Laird (Reference Johnson-Laird and Gazzaniga1994), and it has been tested in many brain-imaging studies of reasoning. Although reasoning tasks are typically associated with left hemisphere activation, the results have actually been mixed, with many studies showing activation in both hemispheres, and on the whole, these brain-imaging studies do not distinguish between current theories of reasoning (see Goel [Reference Goel2007] for a review). An absence of neural predictions for Bayesian modeling could reflect a correct understanding of how best to use this tool. It would be better to make as few neural or representational assumptions as possible, than to make unfounded ones.

The fact that Bayesian models are rational does not imply that researchers who use them are irrational fundamentalists. Bayesian modeling is simply a new tool with advantages and disadvantages like any other kind of modeling. J&L make a vivid case for some disadvantages, but greatly understate the advantages of models that explain how prior hypotheses are put together with new observations, using a minimum number of unfounded assumptions. Still, J&L deserve credit for fostering a debate on these important models.