The many faces of Bayesian models

I will come clean to begin with. I like the general idea of Bayesian inductive reasoning – it is so clearly on the mark that it almost appears tautological. But as soon as actual numbers are put into actual equations, my confidence starts to melt to the extent that the numbers are often guesses. I find that many people have some sort of switch in their thinking so that when they are doing mechanical operations on numbers (solving equations) they appear to stop doing any critical thinking (evaluating ideas). A case in point is the way Bayesian equations were trusted, without critical examination of the priors fed into them, led in part to the recent credit crunch. So I whole-heartedly endorse the spirit of Bayesian logic but am suspicious of its practice.

The other thing that I have to declare is that I distrust people who appear to be squeamish about living things, people who want to understand biological systems without taking any notice of the biological aspects of the systems, want to understand thought without understanding brains.

So you can understand why I enjoyed Jones and Love’s paper on Bayesian Fundamentalism and Bayesian Enlightenment (pdf). It looks at both what is so promising about Bayes’ Rule, which they call Enlightened Bayesian approach, and what is so disturbing, which they call Bayesian Fundamentalism.

What is meant by these terms –

“… placing too much emphasis on mathematical and computational power at the expense of theoretical development. In particular, there has been a considerable amount of work whose primary goal is to demonstrate that human behavior in some task is rational with respect to a particular choice of Bayesian model. We refer to this school of thought as Bayesian Fundamentalism, because it strictly adheres to the tenet that human behavior can be explained through rational analysis—once the correct probabilistic interpretation of the task environment has been identified—without recourse to process, representation, resource limitations, or physiological or developmental data. ”

“… the Enlightened Bayesian approach, because it goes beyond the dogma of pure rational analysis and actively attempts to integrate with other avenues of inquiry in cognitive science. A critical distinction between Bayesian Fundamentalism and Bayesian Enlightenment is that the latter considers the elements of a Bayesian model as claims regarding psychological process and representation, rather than mathematical conveniences made by the modeler for the purpose of deriving computational- level predictions. Bayesian Enlightenment thus treats Bayesian models as making both rational and mechanistic commitments, and it takes as a goal the joint evaluation of both. ”

There are other uses of Bayesian logic –

“… Agnostic Bayesian research is concerned with inferential methods for deciding among scientific models based on empirical data. This line of research has developed powerful tools for data analysis, but as with other such tools (e.g., analysis of variance, factor analysis) they are not intended as models of cognition itself. Because it has no position on whether the Bayesian framework is useful for describing cognition, Agnostic Bayes is not a topic of the present article. Likewise, research in pure Artificial Intelligence that uses Bayesian methods without regard for potential correspondence with biological systems is beyond the scope of this article. ”

Metaphors are indispensable in science, giving structure, understanding, parallels, insights and new ideas. But researchers must be clear not to mistake metaphors for the theories.

Bayesian Fundamentalism clearly rejects mechanism and shares this with Behaviorism.

“The core assumption is that one can predict behavior by calculating what is optimal in any given situation. Thus, the theory is cast entirely at the computational level, without recourse to mechanistic (i.e., algorithmic or implementational) levels of explanation. As a meta-scientific stance, this is a very strong position. It asserts that a wide range of modes of inquiry and explanation are essentially irrelevant to understanding cognition. In this regard, the Bayesian program has much in common with Behaviorism. … Importantly, the limitation is not just on what types of explanations are considered meaningful, but also on what is considered worthy of explanation – that is, what scientific questions are worth pursuing and what types of evidence are viewed as informative.”

Likewise it has similarities with Evolutionary Psychology in the temptation for just-so stories.

“Bayesian Fundamentalism is vulnerable to many of the criticisms that have been leveled at evolutionary psychology. Indeed, we argue that notions of optimality in evolutionary psychology are more complete and properly constrained than those forwarded by Bayesian Fundamentalists because evolutionary psychology considers other processes than simple adaptation. Because it is mechanisms that evolve, not behaviors, Bayesian Fundamentalism’s assertions of optimality provide little theoretical grounding and are circular in a number of cases.”

“Whereas previous work in the heuristics-and-biases tradition cast the bulk of cognition as irrational using a fairly simplistic notion of rationality, Bayesian Fundamentalism finds rationality to be ubiquitous based on under-constrained notions of rationality. … Completely sidestepping mechanistic considerations when considering optimality leads to absurd conclusions. To illustrate, it may not be optimal or evolutionarily advantageous to ever age, become infertile, and die, but these outcomes are universal and follow from biological constraints. It would be absurd to seriously propose an optimal biological entity that is not bounded by these biological and physical realities, but this is exactly the reasoning Bayesian Fundamentalists follow when formulating theories of cognition. ”

There are also problems with what optimal means for developing minds.

On the other hand, Enlightened Bayesian models can be taken seriously as psychological theories.

“According to the Fundamentalist Bayesian view, the hypotheses and their prior distribution correspond to the true environmental probabilities within the domain of study. However, as far as predicting behaviour is concerned, all that should matter is what the subject believes (either implicity or explicitly) are the true probabilites. … the question of whether people have veridical mental models of their environment can be separated from the question of whether people reason and act optimally with respect to whatever models they have.”

“The Bayesian approach suggests that learning involves working backward from sense data to compute posterior probabilities over latent variables in the environment, and then determining optimal action with respect to those probabilities. This can be contrasted with the more purely feed-forward nature of most extant model, which learn mappings from stimuli to behavior and use feedback from the environment to directly alter the internal parameters that determine those mappings.”

“Prior distributions offer another opportunity for psychological inquiry within the Bayesian framework. In addition to the obvious connections to biases in beliefs and expectations, the nature of the prior has potential ties to questions of representation. … Conjugate priors are a common assumption made by Bayesian modelers, but this assumption is generally made solely for mathematical convenience of the modeler, rather than for any psychological reason. However, considering a conjugate prior as part of the psychological theory leads to the intriguing possibility that the parameters of the conjugate family constitute the information that is explicitly represented and updated in the brain. ”

Even the algorithms that are used by Bayesians for approximate predictions of difficult calculations may give useful ideas of how the brain may make similar approximations. So Bayesian ideas have a great deal to offer in the context of a mechanistic metaphor.

Source:

Jones, M. & Love, B.C. (in press). Bayesian Fundamentalism or Enlightenment? On the Explanatory Status and Theoretical Contributions of Bayesian Models of Cognition. Behavioral and Brain Sciences (target article).

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