Jones & Love (J&L) argue that Bayesian approaches to human behavior should attend more closely to cognitive and neural mechanisms. Because mechanisms play such an important role in their target article, it is important to get a clear idea of what mechanisms are and what they are good for. J&L unfortunately do not clarify the term. They get closest when, in section 5.1, they mention the “notion of mechanism (i.e., process or representation)” (para. 3, emphasis J&L's). This treatment is, in our view, less accurate than would be needed to support the strong claims the target article makes with regard to the status of Bayesian approaches to cognition. When the concepts of mechanism and process are fleshed out, these claims might well turn out to be untenable.
Roughly, processes and mechanisms relate as follows. A process concerns the change of a system over time. The easiest way to think about this is as a path through a set of possible states the system can be in. A process model is a description of this path, detailing how each new state (or its probability) depends on its previous state(s). In the behavioral sciences, such a model can often be represented by a flowchart. A mechanism, by contrast, is not a process but a system. It typically has parts that work together to implement an input-output relation. For instance, smoking (input) robustly produces lung cancer (output), through a causal mechanism (smoke brings tar into the lungs which leads to mutations). A mechanistic model is a representation of the way the parts of the system influence one another. Typically, this is represented as a directed graph or a circuit diagram. Mechanisms are closely tied to the notion of function, because they are often studied and discovered by pursuing questions of the “how does this work?” variety (e.g., “how does smoke cause cancer?”).
Now, a Bayesian model is a process model, not a mechanistic model. This is not, as J&L believe, because “the Bayesian metaphor is tied to a mathematical ideal and thus eschews mechanism altogether” (sect. 2.2, para. 3), but simply because it describes how a rational agent moves through an abstract state-space of beliefs (probabilities of hypotheses) when confronted with evidence (data): all the model says is how a rational agent is to move to new belief state at t+1, given the prior belief state and evidence available at time t. This has nothing to do with the fact that the model is mathematically formalized. Mechanistic and causal models have mathematical formalizations just as well (e.g., see Pearl Reference Pearl2000). The Bayesian model is simply not a mechanistic model because it is a process model. To argue that the Bayesian model fails to capture mechanisms is much like arguing against relativity theory because it provides no mechanistic detail on how clocks slow down when moved.
Clearly there have to be mechanisms that allow the belief-updating process to run, and these mechanisms are likely to reside in our brain. One may profitably study these mechanisms and even provide support for Bayesian models with that. A good question, for instance, that may receive a mechanistic answer is, “How do people implement belief updating?” (Ma et al. Reference Ma, Beck, Latham and Pouget2006). Note that, by a suitable choice of variables and probabilistic relations, any sequence of belief states can be viewed as resulting from a Bayesian update (cf. Albert Reference Albert, Corfield and Williamson2001). But say that we have independently motivated our starting points and found a convincing fit with the behavioral data of the belief dynamics (e.g., Brown et al. Reference Brown, Wagenmakers and Steyvers2009). J&L then seem to suggest how this model might be given a mechanistic underpinning when they say that “belief updating of Bayes’ Rule [amounts] to nothing more than vote counting” (sect. 7, para. 3). To us, the vote-counting idea seems just about right, since vote counting is about all that neurons can do if they are supposed to be ultimately implementing the process. We would add that mechanisms might also support the Bayesian account by providing independent motivations for choosing the variables and relations that make up the model.
Another good question is, “Why do people deviate from optimality in circumstance X?” The Bayesian model cannot explain such deviations directly, since it presupposes optimality. However, without a clear definition of optimality, as given by the Bayesian model, it would be impossible to detect or define such deviations in the first place: Without the presence of rationality, the concept of bounded rationality cannot exist. What's more, suboptimal behavior can be elucidated by giving it the semblance of optimality within a Bayesian model. Those models then suggest what potentially irrational assumptions real agents make; the Bayesian models of reasoning behavior (Oaksford & Chater Reference Oaksford and Chater2007) are a case in point.
J&L are not satisfied by this type of mechanistic support for Bayesian models; they argue that mechanistic theories should constrain the Bayesian model. However, it is unclear why exactly we should believe this. Surely, it does not matter for the empirical adequacy of the Bayesian process models whether peoples’ beliefs are physically realized as activation networks in their frontal lobe, as global properties of their brain states, or as bursts of currents running in their big left toe. What matters is that the behavioral data are fitted within an independently motivated and predictively accurate model. In fact, if it turned out that dualism were correct after all, and belief revision actually went on in Cartesian mental stuff, that would not hurt the Bayesian analysis one bit – as long as the mental stuff updated its beliefs properly. Thus, the relation between Bayesian explanation and mechanistic accounts is asymmetric: While the finding that there is a mechanistic realization of Bayesian belief revision supports the Bayesian view, not finding such a mechanistic realization does not refute the theory. The only facts that can refute the Bayesian explanation are empirical facts about human behavior.
Jones & Love (J&L) argue that Bayesian approaches to human behavior should attend more closely to cognitive and neural mechanisms. Because mechanisms play such an important role in their target article, it is important to get a clear idea of what mechanisms are and what they are good for. J&L unfortunately do not clarify the term. They get closest when, in section 5.1, they mention the “notion of mechanism (i.e., process or representation)” (para. 3, emphasis J&L's). This treatment is, in our view, less accurate than would be needed to support the strong claims the target article makes with regard to the status of Bayesian approaches to cognition. When the concepts of mechanism and process are fleshed out, these claims might well turn out to be untenable.
Roughly, processes and mechanisms relate as follows. A process concerns the change of a system over time. The easiest way to think about this is as a path through a set of possible states the system can be in. A process model is a description of this path, detailing how each new state (or its probability) depends on its previous state(s). In the behavioral sciences, such a model can often be represented by a flowchart. A mechanism, by contrast, is not a process but a system. It typically has parts that work together to implement an input-output relation. For instance, smoking (input) robustly produces lung cancer (output), through a causal mechanism (smoke brings tar into the lungs which leads to mutations). A mechanistic model is a representation of the way the parts of the system influence one another. Typically, this is represented as a directed graph or a circuit diagram. Mechanisms are closely tied to the notion of function, because they are often studied and discovered by pursuing questions of the “how does this work?” variety (e.g., “how does smoke cause cancer?”).
Now, a Bayesian model is a process model, not a mechanistic model. This is not, as J&L believe, because “the Bayesian metaphor is tied to a mathematical ideal and thus eschews mechanism altogether” (sect. 2.2, para. 3), but simply because it describes how a rational agent moves through an abstract state-space of beliefs (probabilities of hypotheses) when confronted with evidence (data): all the model says is how a rational agent is to move to new belief state at t+1, given the prior belief state and evidence available at time t. This has nothing to do with the fact that the model is mathematically formalized. Mechanistic and causal models have mathematical formalizations just as well (e.g., see Pearl Reference Pearl2000). The Bayesian model is simply not a mechanistic model because it is a process model. To argue that the Bayesian model fails to capture mechanisms is much like arguing against relativity theory because it provides no mechanistic detail on how clocks slow down when moved.
Clearly there have to be mechanisms that allow the belief-updating process to run, and these mechanisms are likely to reside in our brain. One may profitably study these mechanisms and even provide support for Bayesian models with that. A good question, for instance, that may receive a mechanistic answer is, “How do people implement belief updating?” (Ma et al. Reference Ma, Beck, Latham and Pouget2006). Note that, by a suitable choice of variables and probabilistic relations, any sequence of belief states can be viewed as resulting from a Bayesian update (cf. Albert Reference Albert, Corfield and Williamson2001). But say that we have independently motivated our starting points and found a convincing fit with the behavioral data of the belief dynamics (e.g., Brown et al. Reference Brown, Wagenmakers and Steyvers2009). J&L then seem to suggest how this model might be given a mechanistic underpinning when they say that “belief updating of Bayes’ Rule [amounts] to nothing more than vote counting” (sect. 7, para. 3). To us, the vote-counting idea seems just about right, since vote counting is about all that neurons can do if they are supposed to be ultimately implementing the process. We would add that mechanisms might also support the Bayesian account by providing independent motivations for choosing the variables and relations that make up the model.
Another good question is, “Why do people deviate from optimality in circumstance X?” The Bayesian model cannot explain such deviations directly, since it presupposes optimality. However, without a clear definition of optimality, as given by the Bayesian model, it would be impossible to detect or define such deviations in the first place: Without the presence of rationality, the concept of bounded rationality cannot exist. What's more, suboptimal behavior can be elucidated by giving it the semblance of optimality within a Bayesian model. Those models then suggest what potentially irrational assumptions real agents make; the Bayesian models of reasoning behavior (Oaksford & Chater Reference Oaksford and Chater2007) are a case in point.
J&L are not satisfied by this type of mechanistic support for Bayesian models; they argue that mechanistic theories should constrain the Bayesian model. However, it is unclear why exactly we should believe this. Surely, it does not matter for the empirical adequacy of the Bayesian process models whether peoples’ beliefs are physically realized as activation networks in their frontal lobe, as global properties of their brain states, or as bursts of currents running in their big left toe. What matters is that the behavioral data are fitted within an independently motivated and predictively accurate model. In fact, if it turned out that dualism were correct after all, and belief revision actually went on in Cartesian mental stuff, that would not hurt the Bayesian analysis one bit – as long as the mental stuff updated its beliefs properly. Thus, the relation between Bayesian explanation and mechanistic accounts is asymmetric: While the finding that there is a mechanistic realization of Bayesian belief revision supports the Bayesian view, not finding such a mechanistic realization does not refute the theory. The only facts that can refute the Bayesian explanation are empirical facts about human behavior.