Critique of the Bayesian brain hypothesis

Introduction

Human behavior is driven by incomplete data and methods to turn that data into action and perception. Take, for example, our eyes, which do not actually construct a complete high-resolution picture of our surroundings despite that we experience it so. Instead, that image is filled with noise, missing large chunks, and top of all also inverted. Yet, we can use this incomplete data to navigate the world and successfully perform complex behaviors in it. Based on research in cognitive science, it has been theorized that this results from organisms' innate ability to carry out statistical inference. This hypothesis is commonly referred to as the Bayesian brain hypothesis, and the theories concerning posit that our minds and brains are near-optimal in solving a variety of tasks (Bower and Davis 2012).

As mentioned by Bowers and Davis (2012), this conclusion that human behavior is close to the Bayesian optimal is exciting as it positions our behavior in a surprising and counterintuitive state of actually being optimal. They continue that this surprising claim has gathered a wide array of research during the years but not that much criticism as highlighted by a 2013 paper by Marcus and Davis.

This article aims to collect and review the criticism surrounding the Bayesian approach to the brain. The first part will focus on further introducing the concept of Bayesian inference in the brain. The later parts will aim to review and provide a concise framework of literature on criticism surrounding the Bayesian brain hypothesis.

Introduction to Bayesian theory

Before further analysis of the criticism concerning the Bayesian brain hypothesis, it is worthwhile to cover the fundamentals of both Bayesian statistics as well as their application in cognitive science and neuroscience.

Bayesian probability

In the Bayesian inference models of cognition, cognition is viewed as a process of drawing inferences from observed data (Marcus and Davis 2013). This inference is governed by Bayes's theorem, where A is the hypotheses being investigated, and B is the data that has been observed then states that for every hypothesis,

In this equation, P(Aᵢ| B) is the posterior probability of hypothesis Aᵢ when data B has been observed. P(Aᵢ) is the prior probability of A being true before observing any data, and P(B|Aᵢ) is the likelihood, that is, the conditional probability that B has been observed when Aᵢ is true. This theorem then states that the posterior probability is proportional to the product of prior probability and prior probabilities. In research, the data is usually information available to the human reasoner, priors are the initial state of knowledge, and hypotheses are the conclusion the reasoner draws from these (Bowers and Davis, 2012).

Bayesian brain hypothesis

On the most general level, probabilistic theories of the mind, such as the Bayesian theories in cognitive psychology, make the assumption that brains perform statistical inference on noisy and ambiguous information (Bowers and Davis, 2012). Most Bayesian theories describe the goal of the computation, why that computation is appropriate, and the logic of the strategy. What they don't take into consideration are the mental presentation and processes employed in solving the task. The fundamental goal of the approach is to determine what the optimal solution should look like, and use that to provide important constraints on theories of the brain (Bowers and Davis 2012).

At the same time that the Bayesian approach has gathered interest in cognitive science, the Bayesian approach has also become prominent in neuroscience (Bowers and Davis, 2012). The general idea behind the theories in neuroscience that employ the Bayesian approach is that populations of neurons are capable of representing uncertainty in the form of probability distributions and also capable of performing Bayesian computations (Bowers and Davis, 2012). The criticism surrounding this claim is inspected later in this paper.

Criticism surrounding Bayesian methodology

Criticism on post hoc practices

A notable criticism surrounding Bayesian inference in psychology comes from the appearance of post hoc practices in studies that have aimed to show the mind as a near-optimal engine of probabilistic inference. In their 2013 paper, Marcus and Davis name two closely related problems: task selection and modal selection, as a reason for concern. They see that these two problems undermine the conclusion of cognition being optimal or driven by probabilistic inference.

Criticism of task selection

According to Marcus and Davis (2013), human cognition can seem near-normative when the circumstances are correct while failing to appear so in others. They use a study of physical reasoning by Battaglia, Hamrick, and Tenenbaum as an example (Battaglia et al., 2013). In this study, participants were asked to predict how a tower of blocks would fall. Based on these results, the researchers proposed that humans' physical judgments are a form of probabilistic inference. However, according to Marcus and Davis, a substantial amount of previous studies have shown different results for other physical judgments. The aforementioned example highlights how research surrounding Bayesian inference suffers from generalizability: models fit a subset of tasks of the same problem space. According to Marcus and Davis, this could be the result of probabilistic-cognition literature disproportionately reporting success leading to a distorted perception of the applicability of these approaches.

Marcus and Davis continue that this risk of favoring probabilistic theories of cognition is elevated by the practice of selecting from a broader range of domains instead of diving deeper into one challenging domain. They conclude their criticism of task selection in Bayesian inference by proposing that an attempt to understand the competing mechanisms would possibly be a more enlightening approach.

Criticism of model selection

Related to the problem of task selection is the problem of selecting the models. Every model depends heavily on the choice of probabilities which can come from real-world frequencies, experimental subjects' judgments, and mathematical models (Marcus and Davis, 2013). In addition to the selection of probabilities, a number of other parameters need to be set either by basing the model on real-world statistics; by choosing the model or tuning the parameters to better fit the experiment at hand, or by using purely theoretical considerations, which can sometimes be quite arbitrary.

Each of these choices for constructing a model can become problematic for the model's real applicability (Marcus and Davis, 2013). Real-world frequencies, for example, maybe heavily dependent on what dataset is used. Another subject of problems is how the fit of the model to a certain data set is contingent on how the priors are chosen. To highlight this, Marcus and Davis use Griffiths and Tenenbaum's (2006) study where participants were asked to predict the length of poems, of which they were read a small section and then provide the information on what line that was. The priors for this study were based on the distribution of poem lengths in an online corpus of poetry. The results of the study made Griffith and Tenenbaum suggest that "people's judgements for . . . poem lengths . . . were indistinguishable from optimal Bayesian predictions based on the empirical prior distributions". However, Marcus and Davis (2013) see that the actual fit and the model was actually not in fact as close as the study had suggested, as "it requires no great knowledge of poetry to predict that a poem whose fifth line has been quoted must have at least five lines". The actual fit of the model was overestimated because of how priors were chosen.

Marcus and Davis (2013) conclude their criticism by arguing that probabilistic models such as the Bayesian approach have not yielded a robust account of cognition that would be applicable across tasks. Yet, they also see the Bayesian approach as a useful tool, albeit not one that one-size-fits-all solution.

Bayesian theories against traditional non-Bayesian approaches

While Marcus and Davis' (2013) challenge the robustness of the Bayesian approach and how models and tasks are selected, it does not contrast the probabilistic approach to other approaches of studying the brain and mind. How promising the Bayesian approach is when compared to more traditional non-Bayesian approaches to studying mind and brain is discussed in Bowers and Davis' 2012 paper.

Bower and Davis (2012) argue that the evidence supporting the Bayesian approach is rather weak, with proponents of the Bayesian approach having reached quite different conclusions on the basis of the same evidence. Similar to Marcus and Davis (2013), Bowers and Davis also see that the selection of priors and likelihoods can arbitrarily be altered to provide a better fit, providing an additional point that it makes Bayesian models difficult to falsify. The paper also argues that the Bayesian approach is too rarely compared to the non-Bayesian approaches, such as heuristic or adaptive theories of the mind. As the last major point of critique, Bowers and Davis argue that there is very little data for supporting the notion of collections of neurons performing Bayesian computations.

Bowers and Davis (2012) conclude their paper by arguing that it is not clear how the Bayesian approach provides additional insights into the nature of mind and brain when compared to non-Bayesian approaches. They instead see that the result of the Bayesian approach has been a collection of Bayesian just-so stories, in which mathematical analyses can be used to explain almost any behavior as optimal.

Criticism against Bayesian theorizing

Equally strong criticism has been raised on how Bayesian approaches are used to theorize in cognitive science. In their 2011 article, Jones and Love (2011) subdivide Bayesian theories into two philosophies: Bayesian fundamentalism and Bayesian enlightenment. Bayesian fundamentalism firmly clings to the principle that human behavior is explainable through rational analysis: once a given task is correctly reduced to environmental statistics and goals, human behavior in that task will be found to be rational. This approach places too much emphasis on the mathematical and computational power of probabilistic inference, without moving towards more substantial theoretical development (Jones and Love, 2011). According to Jones and Love (2011), most of the research surrounding the Bayesian approach falls into the category of Bayesian fundamentalism.

In contrast to Bayesian fundamentalism, Jones and Love's Bayesian enlightenment goes beyond the dogma of rational analysis, actively integrating with other avenues or inquiries in cognitive science (Jones and Love, 2011). They see this as an approach that does aim towards more substantial theoretical development.

Jones and Love's (2011) view the Enlightened Bayesian view as being capable of taking the more interesting aspect of the Bayesian approach; which include the algorithms by which inference is carried out and the representations on which those algorithms operate; seriously as psychological constructs and evaluate them according to theoretical merit rather than mathematical convenience. They conclude their criticism on Bayesian theorizing by predicting that the Bayesian approach has much to contribute as long as it is developed in a way that does not eliminate the psychology from psychological models.

Conclusion

The probabilistic approach to the brain can be seen as a widely applicable approach, but one of which research and results need further inspection and review, as can be concluded from the criticism reviewed in this paper. The criticism has primarily focused on how the selection of models and tasks has contributed to overpromising models. Another large part of criticism has been the subject of how Bayesian methods are used to theorize in cognitive science. Despite the reviewed criticisms, the Bayesian approach is seen as a promising approach, as long as the limitations of it are understood and it continues moving towards more substantial theoretical development.

References

Battaglia, P. W., Hamrick, J. B., & Tenenbaum, J. B. (2013). Simulation as an engine of physical scene understanding. Proceedings of the National Academy of Sciences, 110(45), 18327–18.
Bowers, J. S., & Davis, C. J. (2012). Bayesian just-so stories in psychology and neuroscience. Psychological Bulletin, 138(3), 389.
Jones, M., & Love, B. C. (2011). Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behavioral and brain sciences, 34(4), 169.
Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological science, 17(9), 767–773.
Marcus, G. F., & Davis, E. (2013). How robust are probabilistic models of higher-level cognition?. Psychological science, 24(12), 2351–2360.