Bayesian models of cognition

Bayesian models of cognition describe the mind as performing probabilistic inference: combining prior beliefs with new evidence according to Bayes’ rule to reach updated beliefs, and acting to maximise expected utility. Such “rational” models have been applied to perception, reasoning and learning. In reasoning, for example, the everyday conditional “if p then q” is modelled as the probability of q given p rather than as a rule of logic (Cruz et al., 2015). Their standing is contested. Critics argue that they are unconstrained by data about mental processes, often restate existing mechanistic theories (Jones & Love, 2011), and can be fitted to almost any result because priors, likelihoods and utilities can be adjusted after the fact (Bowers & Davis, 2012). Defenders reply that the critiques misdescribe the aims of Bayesian modelling and fail to compare it with specific alternatives (Griffiths et al., 2012).

History

Not covered by the research: rational analysis (Anderson, 1990) and the growth of Bayesian modelling in the 2000s.

Core concepts

Rational models and Marr’s levels

Marr distinguished three levels of explanation: the computational level (what problem is solved and why), the algorithmic level (the representations and processes that solve it) and the implementational level (the physical mechanism). Cooper and Peebles argue that explanation starting at this level alone, as purely Bayesian accounts do, has fundamental limitations and needs to be coupled to the level of algorithms and representations and to a cognitive architecture (Cooper & Peebles, 2015). Love likewise notes that the computational level gives weak constraint, and that people can be suboptimal for reasons other than limited capacity (Love, 2015). The Methods article discusses Marr’s levels further.

Normative and descriptive models

Tauber and colleagues propose separating two uses of Bayesian models. Normative models claim that people behave optimally given their environment; descriptive models use the Bayesian machinery to describe behaviour without any claim of optimality. They argue that conflating the two causes confusion in the debate (Tauber et al., 2017).

Questions, controversies, and new developments

Are Bayesian models too flexible?

Jones and Love argued in 2011 that rational Bayesian models are unconstrained by data on mental processes and often recapitulate existing mechanistic theories in new terms (Jones & Love, 2011). Bowers and Davis argued that the evidence for Bayesian theories in psychology is weak because priors, likelihoods and utilities can be altered to fit the data, which makes the models unfalsifiable, and that they rarely outperform simpler alternatives (Bowers & Davis, 2012). Marcus and Davis argued that the rational-probabilistic approach is less promising than widely believed because of such post hoc practices (Marcus & Davis, 2013).

Griffiths, Chater, Norris and Pouget replied that the critique misstates what motivates Bayesian modelling and does not compare it against specific alternatives (Griffiths et al., 2012). Hahn argued that the criticisms cannot be sustained across the diversity of Bayesian applications and are framed at the wrong level of generality (Hahn, 2014).

The dispute is contested.

Is optimality well defined?

Brette rejects framing perception as statistical inference over a model fixed in advance, arguing that optimality is often ill defined (Brette, 2018). This connects to the question of whether perception is constructive inference at all, discussed in Perception.

Replication record

Not covered by the research: tests of specific Bayesian models against process models after 2012.

Broader connections

Bayesian accounts are one of the families compared in Architecture of the mind. In reasoning, they compete with mental logic and mental models; mental-model theorists credit them as the first attempt to explain reasoning without logic, but argue that they do not handle statements about possibility (Johnson-Laird & Ragni, 2024).

Further reading

• Jones and Love (2011): the critique that started the recent debate.
• Griffiths et al. (2012): the defenders’ reply.
• Tauber et al. (2017): separating normative from descriptive Bayesian models.